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Computational problem used in cryptography
Short integer solution (SIS) and ring-SIS problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based
Short integer solution problem
Short_integer_solution_problem
Method to solve optimization problems
variables are required to be integers, then the problem is called an integer programming (IP) or integer linear programming (ILP) problem. In contrast to linear
Linear_programming
Mathematical optimization problem restricted to integers
An integer programming, also known as integer optimization, problem is a mathematical optimization or feasibility program in which some or all of the variables
Integer_programming
Mathematical problem in number theory
cattle problem (or the problema bovinum or problema Archimedis) is a problem in Diophantine analysis, the study of polynomial equations with integer solutions
Archimedes's_cattle_problem
Optimization problem in computer science
Learning with errors Short integer solution problem Khot, Subhash (2005). "Hardness of approximating the shortest vector problem in lattices". J. ACM
Lattice_problem
Computer software bug occurring in 2038
systems. Modern systems and software updates address this problem by using signed 64-bit integers, which will take 292 billion years to overflow—approximately
Year_2038_problem
Unsolved problem in computer science
Unsolved problem in computer science If the solution to a problem can be checked in polynomial time, must the problem be solvable in polynomial time? More
P_versus_NP_problem
NP-hard problem in combinatorial optimization
Corporation, who expressed the problem as an integer linear program and developed the cutting plane method for its solution. They wrote what is considered
Travelling_salesman_problem
On solvability of Diophantine equations
principal contributors to its solution). When all coefficients and variables are restricted to be positive integers, the related problem of polynomial identity
Hilbert's_tenth_problem
Decision problem in computer science
sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers and
Subset_sum_problem
Problem a computer might be able to solve
science, a problem is one that asks for a solution in terms of an algorithm. For example, the problem of factoring "Given a positive integer n, find a
Computational_problem
{\displaystyle A,B,C} must share some prime factor. Brocard's problem: are there any integer solutions to n ! + 1 = m 2 {\displaystyle n!+1=m^{2}} other than
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Problem in combinatorial optimization
Knapsack Problem Archived 14 February 2015 at the Wayback Machine Optimizing Three-Dimensional Bin Packing Knapsack Integer Programming Solution in Python
Knapsack_problem
Problem of finding the best feasible solution
economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two
Optimization_problem
Solving an optimization problem with a quadratic objective function
x will need to take on integer values. This leads to the formulation of a mixed-integer quadratic programming (MIQP) problem. Applications of MIQP include
Quadratic_programming
Topics referred to by the same term
state SIS (file format), Symbian OS filename extension Short integer solution problem, a problem in lattice-based cryptography Single-instance storage
Sis
Sum of inverse squares of natural numbers
1741. The solution to this problem can be used to estimate the probability that two large random numbers are coprime. Two random integers in the range
Basel_problem
Optimization problem
The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a
Vehicle_routing_problem
This is a list of notable integer sequences with links to their entries in the On-Line Encyclopedia of Integer Sequences. OEIS core sequences Index to
List_of_integer_sequences
Triangle with integer side lengths
positive integers can serve as the side lengths of an integer triangle as long as it satisfies the triangle inequality: the longest side is shorter than the
Integer_triangle
Complexity class
known as the travelling salesman problem—is NP-hard. The subset sum problem is another example: given a set of integers, does any non-empty subset of them
NP-hardness
17th-century conjecture proved by Andrew Wiles in 1994
developed methods for the solution of some kinds of Diophantine equations. A typical Diophantine problem is to find two integers x and y such that their
Fermat's_Last_Theorem
In mathematics, when is n!+1 a square
Unsolved problem in mathematics Does n ! + 1 = m 2 {\displaystyle n!+1=m^{2}} have integer solutions other than n = 4 , 5 , 7 {\displaystyle n=4,5,7}
Brocard's_problem
Polynomial equation whose integer solutions are sought
Diophantine equation is a polynomial equation with integer coefficients, for which only integer solutions are of interest. A linear Diophantine equation equates
Diophantine_equation
Complexity class
the integers that have the same total. This problem is contained in PPP, but it is not known if it is PPP-complete. The constrained-SIS (short integer solution)
PPP_(complexity)
Classical problem in combinatorics
to form an integer solution. The primal-dual algorithm for the set cover problem is an iterative method that constructs feasible solutions to both the
Set_cover_problem
Mathematical puzzle
measure any integer amount up to the sum of the volumes. As shown in the previous section, we can construct the solution to the problem from the desired
Water_pouring_puzzle
Arithmetic operation
the Greatest Unsolved Problem in Mathematics. New York City: Penguin Books. ISBN 978-0-452-28525-5. Weisstein, Eric W. "Integer Division". MathWorld.
Division_(mathematics)
NP-complete problem in computer science
science, the partition problem, or number partitioning, is the task of deciding whether a given multiset S of positive integers can be partitioned into
Partition_problem
How many integer lattice points there are in a circle
In mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and
Gauss_circle_problem
Mathematical problem
be obtained using only coins of 3 and 5 units is 7 units. The solution to this problem for a given set of coin denominations is called the Frobenius number
Coin_problem
On divisibility among sets of integers
Znám's problem asks which sets of integers have the property that each integer in the set is a proper divisor of the product of the other integers in the
Znám's_problem
Optimization technique for solving (mixed) integer linear programs
Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not necessarily
Cutting-plane_method
Mathematical problem in number theory
In number theory, Waring's problem asks whether each natural number k has an associated positive integer s such that every natural number is the sum of
Waring's_problem
Combinatorial optimization problem
polynomial. If the weights are integers, and all weights are at most C (where C>1 is some integer), then the problem can be solved in O ( m n log (
Assignment_problem
Problem in geometry
A006533". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Honsberger, Ross (1973). "9. A Problem in Combinatorics". Mathematical Gems.
Moser's_circle_problem
Initial set of valid possible values
including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has
Feasible_region
Theorem in geometric topology
the Betti numbers, which associate to any manifold a list of nonnegative integers. Riemann showed that a closed connected two-dimensional manifold is fully
Poincaré_conjecture
Complex number whose real and imaginary parts are both integers
number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition and
Gaussian_integer
Mathematical problem in operations research
problem reducible to the knapsack problem. The problem can be formulated as an integer linear programming problem. A paper machine can produce an unlimited
Cutting_stock_problem
Problem of inverting exponentiation in groups
logarithm problem. Other base-10 logarithms in the real numbers are not instances of the discrete logarithm problem, because they involve non-integer exponents
Discrete_logarithm
Unsolved problem about sums of powers
In mathematics, the Prouhet–Tarry–Escott problem asks for two disjoint multisets A and B of n integers each, whose first k power sum symmetric polynomials
Prouhet–Tarry–Escott_problem
On unit fractions adding to 4/n
{1}{y}}+{\tfrac {1}{z}}} have a positive integer solution for every integer n ≥ 2 {\displaystyle n\geq 2} ? More unsolved problems in mathematics The Erdős–Straus
Erdős–Straus_conjecture
Matrix form in linear algebra
matrices over the integers Z {\displaystyle \mathbb {Z} } . Just as reduced echelon form can be used to solve problems about the solution to the linear system
Hermite_normal_form
Branch of numerical optimization
on finding the global solutions of an optimization problem whilst providing theoretical guarantees that the reported solution is indeed the global one
Deterministic global optimization
Deterministic_global_optimization
Mathematical problem set on a chessboard
queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no
Eight_queens_puzzle
Mathematical and computational problem
of items is clear from the context. A possible integer linear programming formulation of the problem is: where y j = 1 {\displaystyle y_{j}=1} if bin
Bin_packing_problem
Computer arithmetic error
8-bit integer addition of 127 + 1 results in −128, a two's complement of 128). (A solution for this particular problem is to use unsigned integer types
Integer_overflow
Natural number
not semiperfect. 70 is also part of the only nontrivial solution pair to the cannonball problem, along with 24. In Jewish tradition, Ptolemy II Philadelphus
70_(number)
Mathematical algorithm
Kuṭṭaka is an algorithm for finding integer solutions of linear Diophantine equations. A linear Diophantine equation is an equation of the form ax + by
Kuṭṭaka
Mathematical puzzle
studied problems requiring integer solutions in the 3rd century CE. The Euclidean algorithm for greatest common divisor which underlies the solution of such
The_monkey_and_the_coconuts
Mathematical problem
for n {\displaystyle n} being any positive integer. The exercise of working through this problem may be used to explain and demonstrate exponents
Wheat_and_chessboard_problem
23 mathematical problems stated in 1900
Fields Medal in 1966 for his work on the first problem, and the negative solution of the tenth problem in 1970 by Yuri Matiyasevich (completing work by
Hilbert's_problems
Set of objects whose state must satisfy limits
these kinds of problems. Additionally, the Boolean satisfiability problem (SAT), satisfiability modulo theories (SMT), mixed integer programming (MIP)
Constraint satisfaction problem
Constraint_satisfaction_problem
Complexity class
contains the classes PPAD and PWPP. Notable problems in this class include the short integer solution problem. PPAD (standing for "Polynomial time Parity
TFNP
and Tao in 2014. The Erdős discrepancy problem on partial sums of ±1-sequences. Terence Tao announced a solution in September 2015; it was published in
List of conjectures by Paul Erdős
List_of_conjectures_by_Paul_Erdős
On the distribution of prime numbers
sometime be in a position to attempt the rigorous solution of Goldbach's problem, viz., whether every integer is expressible as the sum of two positive prime
Hilbert's_eighth_problem
Subfield of mathematical optimization
feasible solutions is discrete or can be reduced to a discrete set. Typical combinatorial optimization problems are the travelling salesman problem ("TSP")
Combinatorial_optimization
on the traveling salesman problem. The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is
List_of_NP-complete_problems
Problem in number theory
sums of powers, it is an open problem to characterize the numbers that can be expressed as a sum of three cubes of integers, allowing both positive and
Sums_of_three_cubes
Does the plane contains a dense set of points whose distances are all rational
its vertices, and then scaled to make the distances integers. However, like the Erdős–Ulam problem, Harborth's conjecture remains unproven. Anning, Norman
Erdős–Ulam_problem
Root of a quadratic polynomial with a unit leading coefficient
are integers, i.e. quadratic integers are algebraic integers of degree two. Thus quadratic integers are those complex numbers that are solutions of equations
Quadratic_integer
Mathematical counting-out question
used to solve this problem in the general case by performing the first step and then using the solution of the remaining problem. When the index starts
Josephus_problem
Concept in integral mathematics
optimization problem (integer programming) into a related problem that is solvable in polynomial time (linear programming); the solution to the relaxed
Linear_programming_relaxation
List of unsolved computational problems
list of notable unsolved problems in computer science. A problem in computer science is considered unsolved when no solution is known or when experts
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Mathematical riddle
Mathematically, the problem can be formulated as follows: Given an integer m and a set V of positive integers, find the smallest integer z that cannot be
Postage_stamp_problem
Mathematical puzzle
various lengths and heights, or requesting unusual solutions such as cases where all values are integers. Its charm has been attributed to a seeming simplicity
Crossed_ladders_problem
Mathematical puzzle
although there are actually many more correct solutions. The entries in blue are those that use four integers 4 (rather than four digits 4) and the basic
Four_fours
Family of solutions to related differential equations
when solving problems (like Laplace's equation) in cylindrical coordinates. When α {\displaystyle \alpha } is a half-integer, the solutions are called spherical
Bessel_function
River crossing puzzle
London: Routledge & Kegan Paul. pp. 4–5. Alcuin's Transportation Problems and Integer Programming Archived 2011-07-19 at the Wayback Machine, Ralf Borndörfer
Wolf, goat and cabbage problem
Wolf,_goat_and_cabbage_problem
Type of Diophantine equation
nonsquare integer, and integer solutions are sought for x and y. In Cartesian coordinates, the equation is represented by a hyperbola; solutions occur wherever
Pell's_equation
Probability of shared birthdays
Encyclopedia of Integer Sequences. OEIS. Retrieved 17 February 2020. DasGupta, Anirban. "The matching, birthday and the strong birthday problem: a contemporary
Birthday_problem
Mathematical problem of square numbers which are also square-pyramidal
Encyclopedia of Integer Sequences. OEIS Foundation. Weisstein, Eric W. "Square Pyramidal Number". MathWorld. Weisstein, Eric W. "Cannonball Problem". MathWorld
Cannonball_problem
Optimization by removing non-optimal solutions to subproblems
cannot contain the optimal solution. It is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization
Branch_and_bound
Mathematical formula involving a given set of operations
considered as basic and connected by arithmetic operations (+, −, ×, /, and integer powers) and function composition. Commonly, the basic functions that are
Closed-form_expression
Geometry problem on grid points
no-three-in-line problem and then scaling down the integer grid to fit within a unit square produces solutions to the Heilbronn triangle problem where the smallest
No-three-in-line_problem
Metaheuristic method for optimization problems
for solving linear program problems, integer program problems, mixed integer program problems, nonlinear program problems, etc. VNS systematically changes
Variable_neighborhood_search
Seven mathematical problems with a US$1 million prize for each solution
for the first correct solution to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved
Millennium_Prize_Problems
Choosing the fewest coins to make a given amount of money
of the integer knapsack problem, and has applications wider than just currency. It is also the most common variation of the coin change problem, a general
Change-making_problem
Unsolved problem in mathematics
Unsolved problem in mathematics Is it possible to construct a three-by-three magic square from nine distinct integer squares? More unsolved problems in mathematics
Magic_square_of_squares
Solution of some Diophantine equation
hard open problem. The MRDP theorem (so named for the initials of the four principal contributors to its solution) states that a set of integers is Diophantine
Diophantine_set
Natural number
The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-31. Weisstein, Eric W. "36 Officer Problem". MathWorld. Retrieved 2020-08-21
36_(number)
Natural number
Seventeen is the longest sequence for which a solution exists in the irregularity of distributions problem. Where Pythagoreans saw 17 in between 16 from
17_(number)
Computation modulo a fixed integer
mathematics, modular arithmetic is a system of arithmetic operations for integers, differing from the usual ones in that numbers "wrap around" when reaching
Modular_arithmetic
Concept in modular arithmetic
after dividing ax by the integer m is 1. If a does have an inverse modulo m, then there is an infinite number of solutions of this congruence, which
Modular multiplicative inverse
Modular_multiplicative_inverse
Problem-solving technique and algorithmic paradigm
the problem "find all integers between 1 and 1,000,000 that are evenly divisible by 417" a naive brute-force solution would generate all integers in the
Brute-force_search
Study of mathematical algorithms for optimization problems
optimization, in which an object such as an integer, permutation or graph must be found from a countable set. A problem with continuous variables is known as
Mathematical_optimization
Computational problems no algorithm can solve
Hilbert's tenth problem: the problem of deciding whether a Diophantine equation (multivariable polynomial equation) has a solution in integers. For functions
List_of_undecidable_problems
Family of computing problems
producer-consumer problem (also known as the bounded-buffer problem) is a family of problems described by Edsger W. Dijkstra since 1965. Dijkstra found the solution for
Producer–consumer_problem
3rd-century Greek mathematician
technique to solve problems in arithmetic. The book considers finding integer solutions to equations with integer coefficients, a class of problem presently called
Diophantus
Even integers as sums of two primes
proved that every positive integer is the sum of four squares. See Waring's problem and the related Waring–Goldbach problem on sums of powers of primes
Goldbach's_conjecture
Mathematical investigation of Sudoku
class of Sudoku. The general problem of determining whether a Sudoku puzzle on n2×n2 grids of n×n blocks has a solution is known to be NP-complete. A
Mathematics_of_Sudoku
Mathematical problem set on a chessboard
Hamiltonian path problem is NP-hard in general, on many graphs that occur in practice this heuristic is able to successfully locate a solution in linear time
Knight's_tour
Mathematical concept
Mixed-Integer Linear Program to solve the optimization problem for a weighted sum of the two objectives to calculate a set of Pareto optimal solutions. Applying
Multi-objective_optimization
Inherent difficulty of computational problems
of a solution. If the answer is yes, many important problems can be shown to have more efficient solutions. These include various types of integer programming
Computational complexity theory
Computational_complexity_theory
Mathematical proof technique using contradiction
equation, such as a Diophantine equation, has no solutions. Typically, one shows that if a solution to a problem existed, which in some sense was related to
Proof_by_infinite_descent
Mathematical proof technique
most often used for problems in which a relation between two integers is given, along with a statement to prove about its solutions. In particular, it
Vieta_jumping
Unsolved problem in mathematics
for some integer x. In 1983, Douglas Hensley observed that Büchi's problem is equivalent to the following: Does there exist a positive integer M such that
Büchi's_problem
Natural number
Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A02808 (The composite numbers.)". The On-Line Encyclopedia of Integer Sequences
34_(number)
On existence of a strongly regular graph
2014 as part of a set of problems posed in the DIMACS Conference on Challenges of Identifying Integer Sequences. Other problems in the set include the thrackle
Conway's_99-graph_problem
SHORT INTEGER-SOLUTION-PROBLEM
SHORT INTEGER-SOLUTION-PROBLEM
Female
Scandinavian
Scandinavian form of Old Norse Ingigerðr, INGEGERD means "Ing's enclosure."
Boy/Male
Hindu, Indian
Listener
Surname or Lastname
English and Scottish (now mainly found in Ireland)
English and Scottish (now mainly found in Ireland) : variant spelling of Short.
Female
Swedish
Swedish contracted form of Scandinavian Ingegerd, INGER means "Ing's enclosure."
Boy/Male
Arabic
Prudence; Resolution
Surname or Lastname
English
English : topographic name for someone who lived by a projecting piece of land, from Old English scēat, or a steep slope, from an unattested Old English scēot.
Girl/Female
Arabic, Muslim
Determination; Resolution
Girl/Female
British, English
Tiny; Small
Boy/Male
Hindu, Indian, Marathi
Famous
Surname or Lastname
English
English : nickname from Middle English schort ‘short’.Scottish and northern Irish : reduced Anglicized form of Gaelic Mac an Gheairr, Mac an Ghirr ‘son of the short man’ (see McGirr).
Surname or Lastname
South German and Austrian
South German and Austrian : variant of Hardt 1.English : variant of Hart 1.
Boy/Male
Indian, Sanskrit
Evolution; Progress
Girl/Female
Hindu
Good or Happy condition, Solution
Girl/Female
Muslim
Determination, Resolution
Surname or Lastname
English
English : topographic name for someone who lived by the seashore, Middle English schore.English : topographic name for someone who lived on or by a bank or steep slope, Old English scora. There are minor places named with this word in Lancashire and West Yorkshire, and the surname may also be a habitational name from these.Americanized spelling of Ashkenazic Jewish S(c)hor(r) or Szor, variants of Schauer.
Boy/Male
Hindu
Girl/Female
Tamil
Good or Happy condition, Solution
Boy/Male
Bengali, Indian
Resolution
Girl/Female
Arabic, Muslim
Determination; Resolution
Surname or Lastname
English and German
English and German : unexplained.
SHORT INTEGER-SOLUTION-PROBLEM
SHORT INTEGER-SOLUTION-PROBLEM
Girl/Female
Hindu, Indian
Surname of a Marathi Family
Female
Yiddish
(פֵייגֶע) Yiddish name derived from the word fayg, FEIGE means "fig."
Boy/Male
Muslim
Victorious peace
Boy/Male
Arabic, Muslim
Showing Right Way; Beautiful
Surname or Lastname
English
English : variant spelling of Whitaker.
Male
Greek
(Συμεών): Variant form of Greek SimÅn, from Hebrew Shimon, SYMEON means "hearkening." In the bible, this is the name of several characters, including the second son of Jacob and Leah.Â
Girl/Female
Arabic, Muslim
Adorning the Crown
Girl/Female
British, English, Greek
Follower of Christ
Girl/Female
Biblical
Endowed, endowing.
Girl/Female
Indian
Like King Rama; Good Nature
SHORT INTEGER-SOLUTION-PROBLEM
SHORT INTEGER-SOLUTION-PROBLEM
SHORT INTEGER-SOLUTION-PROBLEM
SHORT INTEGER-SOLUTION-PROBLEM
SHORT INTEGER-SOLUTION-PROBLEM
superl.
Not long; having brief length or linear extension; as, a short distance; a short piece of timber; a short flight.
imp. & p. p.
of Short-circuit
superl.
Breaking or crumbling readily in the mouth; crisp; as, short pastry.
n.
The termination of a disease; resolution.
n.
The act or process of solving; solution; as, the resolution of an equation or problem.
a.
Having short life.
superl.
Engaging or engaged to deliver what is not possessed; as, short contracts; to be short of stock. See The shorts, under Short, n., and To sell short, under Short, adv.
superl.
Not extended in time; having very limited duration; not protracted; as, short breath.
adv.
In a short manner; briefly; limitedly; abruptly; quickly; as, to stop short in one's course; to turn short.
n.
The act of shooting; the discharge of a missile; a shot; as, the shoot of a shuttle.
n.
The state of being dissolved or disintegrated; resolution; disintegration.
p. pr. & vb. n.
of Short-circuit
n.
A short sound, syllable, or vowel.
n.
Short, inferior hemp.
n.
See Exsolution.
n.
To analyse, or determine the strength of, by means of standard solutions. Cf. Standardized solution, under Solution.
a.
Not living or lasting long; being of short continuance; as, a short-lived race of beings; short-lived pleasure; short-lived passion.
superl.
Abrupt; brief; pointed; petulant; as, he gave a short answer to the question.