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Integers that evenly divide their digit reversal
In number theory, reversing the digits of a number n sometimes produces another number m that is divisible by n. This happens trivially when n is a palindromic
Reverse_divisible_number
Natural number
the reverse of any number that is divisible by three (or indeed, any permutation of its digits) is also divisible by three. This divisibility rule works
3
Natural number
centered octagonal number. 1089 is the first nontrivial decimal reverse-divisible number. The next is 2178 (= 1089 × 2 = 8712/4), and they are the only
1089_(number)
Shorthand way of determining whether a given number is divisible by a fixed divisor
A divisibility rule is a shorthand and useful way of determining whether a given integer is divisible by a fixed divisor without performing the division
Divisibility_rule
Unique numeric book identifier since 1970
digits (1st, 3rd, 5th, 7th, 9th, 11th, and 13th), the total will always be divisible by 10 (i.e., end in 0). A 10-digit ISBN is converted to a 13-digit ISBN
ISBN
Natural number
number and the fourth centered hexagonal number. The sum of the squares of the first 37 primes is divisible by 37. 37 is the median value for the second
37_(number)
03, 1 = 13, 8 = 23, 216 = 63) 1007 = number that is the sum of 8 positive 5th powers 1008 = divisible by the number of primes below it 1009 = smallest four-digit
1000_(number)
Natural number
lowest number divisible by both 1 to 9 and 1 to 10, whereas 360 is not the lowest number divisible by 1 to 6 (which 60 is) and is not divisible by 1 to
2000_(number)
Natural number
permutable prime, with ninety-seven. A Pillai prime, because 23! + 1 is divisible by 79, but 79 is not one more than a multiple of 23. A regular prime.
79_(number)
Number divisible only by 1 and itself
polynomial is irreducible based on divisibility of its coefficients by a prime number and its square. The concept of a prime number is so important that it has
Prime_number
Numbers in the Roman numeral system
used a duodecimal rather than a decimal system for fractions, as the divisibility of twelve (12 = 22 × 3) makes it easier to handle the common fractions
Roman_numerals
Standard barcode system used in global trade
checksum digit is the digit which must be added to this checksum to get a number divisible by 10 (i.e. the additive inverse of the checksum, modulo 10). See ISBN-13
International_Article_Number
Extension of the Luhn algorithm
not divisible by 2 by replacing the doubled value at each position with the remainder after dividing the position's value by N which gives odd number remainders
Luhn_mod_N_algorithm
Number that remains the same when its digits are reversed
palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16361) that remains the same when its digits are reversed. In
Palindromic_number
Branch of mathematical logic
Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining
Reverse_mathematics
Natural number
Sophie Germain prime 8695 – decagonal number 8699 – safe prime 8712 – smallest number that is divisible by its reverse: 8712 = 4 × 2178 (excluding palindromes
8000_(number)
Two numbers without shared prime factors
individually—is a prime number, since 1 is their only common divisor. On the other hand, 6 and 9 are not coprime, because they are both divisible by 3. The numerator
Coprime_integers
Quality of zero being an even number
divided by 2 any number of times, and its binary expansion does not contain any 1s, so it always comes first. Although 0 is divisible by 2 more times than
Parity_of_zero
Natural number
33 10176 = smallest (provable) generalized Riesel number in base 10: 10176*10n-1 is always divisible by one of the prime numbers {7, 11, 13, 37} 10201
10,000
Product of numbers from 1 to n
+ 1 {\displaystyle (n-1)!+1} is divisible by n {\displaystyle n} if and only if n {\displaystyle n} is a prime number. For any given integer x {\displaystyle
Factorial
subdivision of quantities into two or more equal parts, any number that is highly divisible has an explicit advantage." Notes: Numbers are shown once only
Convenient_number
Palindromic prime number
prime number 1000000000000066600000000000001 (1030 + 666 × 1014 + 1), a number which reads the same both backwards and forwards and is only divisible by
Belphegor's_prime
Former coin of the United Kingdom and other territories
monetary system (£sd), under which the largest unit was a pound (£), divisible into 20 shillings (s), each worth 12 pence (d), the value of two pre-decimal
Sixpence_(British_coin)
Recursive integer sequence
Press, ISBN 978-0-19-533454-8 Koshy, Thomas & Zhenguang Gao (2011) "Some divisibility properties of Catalan numbers", Mathematical Gazette 95:96–102. Larcombe
Catalan_number
Number without repeated prime factors
square-free integer (or squarefree integer) is an integer that is divisible by no square number other than 1. That is, its prime factorization has exactly one
Square-free_integer
the divisibility rule again, the result can be checked speedily since the addition of all digits gives 54; 5 + 4 = 9—so the number is divisible by 9
Euro_banknotes
Algorithm for determining whether a number is prime
is trial division: given an input number, n {\displaystyle n} , check whether it is divisible by any prime number between 2 and n {\displaystyle {\sqrt
Primality_test
Natural number
composite number; smallest number divisible by the numbers from 1 to 12 (there is no smaller number divisible by the numbers from 1 to 11 since any number divisible
20,000
Number sequence 3,0,2,3,2,5,5,7,10,...
asked if there were any counterexamples to this property. The first P(n) divisible by composite index n was found only in 1982 by William Adams and Daniel
Perrin_number
Condition under which an odd prime is a sum of two squares
})=(aq+bp)^{2}+(ap-bq)^{2}.} 3. If a number which can be written as a sum of two squares is divisible by a number which is not a sum of two squares, then
Fermat's theorem on sums of two squares
Fermat's_theorem_on_sums_of_two_squares
Sufficient condition for polynomial irreducibility
applying a shift, is reversing the order of its coefficients, provided its constant term is nonzero (without which it would be divisible by x anyway). This
Eisenstein's_criterion
Type of algebraic integer
first polynomial is divisible by x2 − 1 when n is odd and by x − 1 when n is even. It has one other real zero, which is a PV number. Dividing either polynomial
Pisot–Vijayaraghavan_number
Methods of error detection and correction in communications
of a polynomial of this sort, and a message has a valid CRC if it is divisible by (i.e. is a multiple of) an agreed-on generator polynomial. As an example
Mathematics of cyclic redundancy checks
Mathematics_of_cyclic_redundancy_checks
Numeral system in combinatorics
checking the divisibility of 4 in base 10 requires looking at only the last two digits, checking the divisibility of any number in factorial number system requires
Factorial_number_system
Type of mathematical proof
Since 1896 = 474 × 4 is divisible by 4, the next Olympics would be in year 474 × 4 + 4 = (474 + 1) × 4, which is also divisible by four, and so on (this
Proof_by_exhaustion
Base-8 numeral representation
(originally occasioned by the number of digits on both hands) yet 8 is a far more complete and commodious number; since it is divisible into halves, quarters
Octal
Open problem on 3x+1 and x/2 functions
example, the only surviving residues mod 32 are 7, 15, 27, and 31. Integers divisible by 3 cannot form a cycle, so these integers do not need to be checked
Collatz_conjecture
Number constructible via compass and straightedge
is a power of two, the splitting field of this polynomial has degree divisible by three, so it does not come from an iterated quadratic extension and
Constructible_number
Payment made by a corporation to its shareholders
payments to Hale in his capacity as a company director but the Appeal Court reversed this judgment and treated the payments as dividends. At the time of payment
Dividend
Specific software-based key for a computer program
characters must all be numbers from 0-8. The sum of the last 7 numbers must be divisible by 7 with no remainder. The fourth character is unchecked. If all checks
Product_key
Mathematical puzzle
fractionating of some discretely divisible quantity, with or without remainders, and a final division into some number of equal parts, possibly with a
The_monkey_and_the_coconuts
Algorithm for generating prime numbers
that are not divisible by any of these prime numbers (and is said to have an associated length Pi). This is because adding Pi to a number does not change
Sieve_of_Pritchard
Mathematical and computational problem
bin packing is that the item sizes form a divisible sequence (also called factored). A special case of divisible item sizes occurs in memory allocation in
Bin_packing_problem
Algorithm for public-key cryptography
of λ(n) for calculating the private exponent d. Since φ(n) is always divisible by λ(n), the algorithm works as well. The possibility of using Euler totient
RSA_cryptosystem
Algorithm for computing greatest common divisors
integers. Since a and b are both divisible by g, every number in the set is divisible by g. In other words, every number of the set is an integer multiple
Euclidean_algorithm
Algebraic structure with a binary operation
with inverse, associativity, and an identity element. Note that each of divisibility and invertibility imply the cancellation property. Magmas with commutativity
Magma_(algebra)
Form of binary-to-text encoding
the source length is not divisible by 3, then the last 4-byte section will contain padding bytes to make it cleanly divisible. These bytes are subtracted
Uuencoding
Family of tile-based games
six, which is divisible by three twice, resulting in two points. Double five at one end and five at the other makes 15, which is divisible by three five
Dominoes
Thought experiment of infinite sets
solution leaves certain rooms empty. (In particular, any room with a number divisible by any prime other than 2 and 3 is empty.) This method can also easily
Hilbert's paradox of the Grand Hotel
Hilbert's_paradox_of_the_Grand_Hotel
Integer side lengths of a right triangle
never even). Exactly one of a, b, c is divisible by 5. The largest number that always divides abc is 60. Any odd number of the form 2m+1, where m is an integer
Pythagorean_triple
Apparent contradiction in metamathematics
For example, "the first natural number" defines the property of being the first natural number, one; and "divisible by exactly two natural numbers" defines
Richard's_paradox
were inconsistent with this concept. For example cobalt and nickel seemed reversed. There were also attempts to understand the relationship between the atomic
History_of_atomic_theory
Integer associated with a civil day
no year 0. Year n CE is a leap year if n is divisible by 4. Year n BCE is a leap year if (n-1) is divisible by 4. Thus the year 1 BCE is a leap year. After
Kali_ahargana
Decentralized digital cryptocurrency
capitalized and lowercase variants without distinction. One bitcoin is divisible to eight decimal places. Units for smaller amounts of bitcoin are the
Bitcoin
Cryptographic algorithm
operation that allows for processing of messages that are not evenly divisible into blocks without resulting in any expansion of the ciphertext, at the
Ciphertext_stealing
Cryptographic algorithm created by Adi Shamir
445,442,\ldots ]} always decreases by 3, so if p {\displaystyle p} were divisible by 3 {\displaystyle 3} she could conclude a 1 ∈ [ 1 , 4 , 7 , … ] {\displaystyle
Shamir's_secret_sharing
Concept in modular arithmetic
Two integers are congruent mod 10 if and only if their difference is divisible by 10, for instance 32 ≡ 2 ( mod 10 ) {\displaystyle 32\equiv 2{\pmod
Modular multiplicative inverse
Modular_multiplicative_inverse
Analytic function on the upper half-plane with a certain behavior under the modular group
construct even unimodular lattices, but here is one way: Let n be an integer divisible by 8 and consider all vectors v in Rn such that 2v has integer coordinates
Modular_form
Property that assigns truth values to k-tuples of individuals
connection between the elements of an n-tuple. For example, the relation "x is divisible by y and z" consists of the set of triples such that when substituted
Finitary_relation
Operating signal for "request to communicate"
adjacent traffic that can interfere) and not expected to use whole-number, divisible-by-five, or otherwise channelized center frequencies. CQ is in constant
CQ_(call)
Divergent sum of positive unit fractions
More generally, any sequence of consecutive integers has a unique member divisible by a greater power of two than all the other sequence members, from which
Harmonic_series_(mathematics)
Alteration in the nucleotide sequence of a genome
mutation is caused by insertion or deletion of a number of nucleotides that is not evenly divisible by three from a DNA sequence. Due to the triplet nature
Mutation
Programming language
7 Checking the divisibility of A by B is_divisible is 0 = mod [A,B] Defining is_prime filter is_prime is 2 = sum eachright is_divisible [pass,count] Count
Nial
Reasoning for mathematical statements
left is an integer multiple of 2, the right expression is by definition divisible by 2. That is, a2 is even, which implies that a must also be even, as
Mathematical_proof
Function in algebra
multiplicity of a zero in complex analysis, the degree of divisibility of a number by a prime number in number theory, and the geometrical concept of contact between
Valuation_(algebra)
symbol is used to indicate that the preceding number measures degrees of arc. | (vertical bar) 1. Divisibility: if m and n are two integers, m ∣ n {\displaystyle
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Controversy regarding copyright
AACS processing key on February 11: Nothing was hacked, cracked or even reverse-engineered btw: I only had to watch the "show" in my own memory. No debugger
AACS encryption key controversy
AACS_encryption_key_controversy
Error-correcting codes
chosen in such a way that c ( x ) {\displaystyle c(x)} becomes exactly divisible by g ( x ) {\displaystyle g(x)} . Then the coefficients of m ( x ) {\displaystyle
Reed–Solomon_error_correction
Equivalence of distributive lattices and set families
natural numbers, ordered with the reverse of the usual divisibility ordering (so x ≤ y when y divides x): any number x can be expressed as the join of
Birkhoff's representation theorem
Birkhoff's_representation_theorem
British card game of the Hearts group for three to six players
with the lowest score after an agreed number of deals (usually divisible by three so that everyone has the same number of turns as dealer). Arnold mentions
Black_Maria_(card_game)
Point on a curve where motion must move backwards
another divisibility condition (giving type A≥4), and a final non-divisibility condition (giving type exactly A4). To see where these extra divisibility conditions
Cusp_(singularity)
Arithmetic operation
(F-division); rarer styles can occur – see modulo operation for the details. Divisibility rules can sometimes be used to quickly determine whether one integer
Division_(mathematics)
Mathematical concept for comparing objects
Reflexive and symmetric: The relation R on Z, defined as aRb ↔ "a − b is divisible by at least one of 2 or 3." Or any dependency relation. Properties definable
Equivalence_relation
=> x * 2); Filtering numbers divisible by 3: value divisibleBy3 = { for (i in 0..100) if (i%3==0) i }; // type of divisibleBy3 is Iterable<Integer> Multiple
Comparison of programming languages (list comprehension)
Comparison_of_programming_languages_(list_comprehension)
Decomposition of a graph into hamiltonion cycles
or Möbius ladder, or when it is a generalized Petersen graph of order divisible by four. There are infinitely many vertex-transitive graphs (graphs in
Hamiltonian_decomposition
Former denomination of sterling coinage
Carolingian monetary system (£sd), under which the largest unit was a pound (£) divisible into 20 shillings (s), each of 12 pence (d). The pre-decimal penny was
Penny (British pre-decimal coin)
Penny_(British_pre-decimal_coin)
Mathematical set with an ordering
which is distinct from it, so g is not maximal. If the number 1 is excluded, while keeping divisibility as ordering on the elements greater than 1, then the
Partially_ordered_set
Pair of polynomial sequences
T_{m}(x)} is divisible by x {\displaystyle x} if m {\displaystyle m} is odd, it follows that T m n ( x ) {\displaystyle T_{mn}(x)} is divisible by T n ( x
Chebyshev_polynomials
Polynomial with reversed root positions
obtained, for instance: A self-reciprocal polynomial of odd degree is divisible by x+1, hence is not irreducible if its degree is > 1. A self-reciprocal
Reciprocal_polynomial
progress on a gameboard delimited by a distinct border, and not further divisible according to the game's rules. Alternatively, a unique position on the
Glossary_of_board_games
System to replace plaintext with ciphertext
QLKBA VAZOA RFPBL UAOAR If the length of the message happens not to be divisible by five, it may be padded at the end with "nulls". These can be any characters
Substitution_cipher
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, ... A Harshad number in base 10 is an integer that is divisible by the sum of its digits (when written in base 10)
List_of_integer_sequences
1997 video game
final score divisible by 10: Sophie is alive, having survived her injuries. In the third ending, obtained by having a score that isn't divisible by 10, a
The House of the Dead (video game)
The_House_of_the_Dead_(video_game)
Set of rules defining correctly structured programs
factors (#'s divisible by, except 1)? ⎕CR 'ProveNonPrime' Z←ProveNonPrime R ⍝Show all factors of an integer R - except 1 and the number itself, ⍝ i.e
APL_syntax_and_symbols
Cosmological dualism in Chinese philosophy
of the opposite field in the droplets shows that they are infinitely divisible depicting there is always yin within yang and always yang within yin and
Yin_and_yang
Spreadsheet software
while 1900 is a year that is divisible by four, years divisible by 100 are not counted as leap years, unless divisible by 400. Microsoft Excel is bug
Lotus_1-2-3
Object or record accepted as payment
, interchangeability). Durable: able to withstand repeated use. Divisible: divisible to small units. Portable: easily carried and transported. Acceptable:
Money
Mathematical use of "for all" and "there exists"
quantification such as There are many integers n < 100, such that n is divisible by 2 or 3 or 5. One possible interpretation mechanism can be obtained
Quantifier_(logic)
Currency of Bermuda
triangular planchets, are minted in gold and silver, and come in denominations divisible by three. In the 20th century, its pound notes were issued in all denominations
Bermudian_dollar
Polynomial equation whose integer solutions are sought
polynomial of degree two in x1, that is zero for x1 = r1. It is thus divisible by x1 − r1. The quotient is linear in x1, and may be solved for expressing
Diophantine_equation
Viruses that cause human parainfluenza
replication and transcription) have a genome nucleotide total that is divisible by the number 6. This has led to the "rule of six" being coined. Exceptions to
Human_parainfluenza_viruses
Race or ethnic-based discrimination
between physical characteristics and moral qualities; that mankind is divisible into superior and inferior stocks. Racism, thus defined, is a modern conception
Racism
Set whose pairs have minima and maxima
Another example is given by the natural numbers, partially ordered by divisibility, for which the supremum is the least common multiple and the infimum
Lattice_(order)
Type of analog linear filter in electronics
of s n {\displaystyle s^{n}} when ( n + 2 ) {\displaystyle (n+2)} is divisible by 4 {\displaystyle 4} . That would be s 2 {\displaystyle s^{2}}
Bessel_filter
Mathematical construct in computer algebra
commonly called lex or plex (for pure lexical ordering). Total degree reverse lexicographical ordering, commonly called degrevlex. Elimination ordering
Gröbner_basis
always divisible by the fact that it is extended, that is to say subject to the spatial condition" (although in the corporeal domain, divisibility has necessarily
René_Guénon
Network of freeways in the United States
south). This numbering system usually holds true even if the local direction of the route does not match the compass directions. Numbers divisible by five
Interstate_Highway_System
Axiom of set theory
choice.) Every free abelian group is projective. Baer's criterion: Every divisible abelian group is injective. Every set is a projective object in the category
Axiom_of_choice
procedure for fair cake-cutting. It involves a certain heterogenous and divisible resource, such as a birthday cake, and n partners with different preferences
Last_diminisher
Hypothetical scenarios upon Quebec independence
le Canada est divisible, le Québec doit être aussi divisible." (This translates as, "If Canada is divisible, Quebec must also be divisible.") Apparently
Partition_of_Quebec
REVERSE DIVISIBLE-NUMBER
REVERSE DIVISIBLE-NUMBER
Boy/Male
Shakespearean
King Henry the Sixth, Part III' Lord Rivers, brother to Lady Grey. 'King Richard III' Earl...
Boy/Male
English
Strict. Restrained. Surname.
Girl/Female
British, English
Beaver-stream
Surname or Lastname
English
English : topographic name for someone who lived on the edge of an escarpment, from Middle English evere ‘edge’, a word that is probably of Old English origin, though unattested.English : patronymic from the Middle English personal name Ever, from Old English Eofor ‘boar’.North German and Dutch : patronymic from Evert.
Boy/Male
English
Name derived from a surname, and only used as a first name since the 19th century.
Girl/Female
Arabic, Muslim
Invisible
Girl/Female
Hindu, Indian, Traditional
Invisible
Surname or Lastname
French
French : variant of Rivière, Rivoire, or Rivier, topographic name for someone living on the banks of a river, French rivier ‘bank’, or habitational name from any of the many places in France named with this word.English : nickname from Middle English revere ‘reiver’, ‘robber’.English : topographic name for someone who lived on the brow of a hill, from a misdivision of the Middle English phrase atter evere ‘at the brow or edge’ (from Old English yfer, efer ‘edge’) or a habitational name from a place named with this phrase, as for example River in West Sussex or Rivar in Wiltshire.Jewish (from Italy) : habitational name from a place in Mantua named Revere.The MA patriot Paul Revere (1734–1818), who in April 1775 undertook a famous ride from Boston to Lexington to warn of the approach of British troops, was a silversmith and instrument maker. He was descended from French Huguenots called Rivoire.
Girl/Female
Tamil
Ikshita | இகà¯à®·à®¿à®¤à®¾
Visible
Ikshita | இகà¯à®·à®¿à®¤à®¾
Male
African
reversed.
Boy/Male
Indian
Visible
Girl/Female
Tamil
Ikshitha | இகà¯à®·à®¿à®¤à®¾
Visible
Ikshitha | இகà¯à®·à®¿à®¤à®¾
Girl/Female
Tamil
Visible
Boy/Male
Hindu, Indian
Invisible
Male
English
Anglicized form of Welsh Rhys, REESE means "ardor, heat of passion."
Girl/Female
Hindu
Visible
Boy/Male
American, British, English
Severe; Strict
Surname or Lastname
English
English : variant spelling of Revell.
Boy/Male
Australian, British, English
Name Derived from a Surname
Girl/Female
Hindu, Indian, Telugu
Invisible
REVERSE DIVISIBLE-NUMBER
REVERSE DIVISIBLE-NUMBER
Surname or Lastname
English
English : habitational name from any of various places so called, the most likely source of the surname being the one in Cheshire near Knutsford. The place name is derived from Old English plūme ‘plum’ + lēah ‘wood’, ‘clearing’.
Boy/Male
Indian, Sanskrit
Wealth
Boy/Male
Hindu, Indian
Strong
Boy/Male
Indian
Unfettered camel
Boy/Male
Bengali, Hindu, Indian, Kannada, Telugu
God of Knowledge; Talented
Girl/Female
Tamil
Ideal
Male
Portuguese
Portuguese name ABÃLIO means "able; proficient; skillful."
Girl/Female
African, Australian, Nigerian
Mother's Daughter
Girl/Female
Muslim
Burning, Flaming
Boy/Male
Gujarati, Hindu, Indian, Kannada
A Name of God Vishnu
REVERSE DIVISIBLE-NUMBER
REVERSE DIVISIBLE-NUMBER
REVERSE DIVISIBLE-NUMBER
REVERSE DIVISIBLE-NUMBER
REVERSE DIVISIBLE-NUMBER
a.
Alt. of Renverse
a.
Invisible.
n.
A divisible substance.
n.
Same as Reverie.
v. i.
To return; to revert.
a.
Indivisible.
n.
One who reveres.
v. t.
To reverse.
n.
That which is indivisible.
a.
Intended to reverse; implying reversal.
a.
Not divisible; incapable of being divided, separated, or broken; not separable into parts.
a.
Capable of being divided; divisible.
a.
Reversed; as, a reverse shell.
a.
The back side; as, the reverse of a drum or trench; the reverse of a medal or coin, that is, the side opposite to the obverse. See Obverse.
v. i.
To change back, as from a soluble to an insoluble state or the reverse; thus, phosphoric acid in certain fertilizers reverts.
n.
One who reverses.
imp. & p. p.
of Revere
v. i.
To become or be reversed.
imp. & p. p.
of Reverse
a.
The act of reversing; complete change; reversal; hence, total change in circumstances or character; especially, a change from better to worse; misfortune; a check or defeat; as, the enemy met with a reverse.