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Repeated sum of a number's digits
The digital root (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing
Digital_root
Figurate number
by a 0 or 5; a final 8 must be preceded by a 2 or 7. In base 10, the digital root of a nonzero triangular number is always 1, 3, 6, or 9. Hence, every
Triangular_number
Mathematical formula
In number theory, the multiplicative digital root of a natural number n {\displaystyle n} in a given number base b {\displaystyle b} is found by multiplying
Multiplicative_digital_root
Sum of a number's digits
decimal digital root of any non-zero integer will be a number in the range 1 to 9, whereas the digit sum can take any value. Digit sums and digital roots
Digit_sum
Numbers obtained by adding the two previous ones
Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related Meertens Other
Fibonacci_sequence
2018 asymmetric board game
Root received positive reviews, and was followed by four expansions. A digital version, developed by Dire Wolf Digital, was released in 2020. In Root
Root_(board_game)
Number divisible only by 1 and itself
Eratosthenes can be sped up by considering only the prime divisors up to the square root of the upper limit. Fibonacci took the innovations from Islamic mathematics
Prime_number
Recursive integer sequence
0 c ( x ) = 1 . {\displaystyle C_{0}=\lim _{x\to 0}c(x)=1\,.} The square root term can be expanded as a power series using the binomial series 1 − 1 −
Catalan_number
Number equal to the sum of its proper divisors
until a single digit (called the digital root) is obtained, always produces the number 1. For example, the digital root of 8128 is 1, because 8 + 1 + 2
Perfect_number
Number raised to the third power
perfect cubes must have digital root 1, 8 or 9. That is their values modulo 9 may be only 0, 1, and 8. Moreover, the digital root of any number's cube can
Cube_(algebra)
Iterative algorithm on numbers
Meertens number Narcissistic number Perfect digit-to-digit invariant Perfect digital invariant Sum-product number For six-digit numbers, i.e. n=6, (1) 6=3×2
Kaprekar's_routine
Product of an integer with itself
a square each side of which has the same number of points as the square root of n; thus, square numbers are a type of figurate numbers (other examples
Square_number
Arithmetic operation
number has a real nth root, which is negative, if n is odd, and no real root if n is even. In the latter case, whichever complex nth root one chooses for x
Exponentiation
Numbers with a certain property involving recursive summation
{\displaystyle b} that eventually reaches 1 when iterated over the perfect digital invariant function for p = 2 {\displaystyle p=2} . The origin of happy
Happy_number
Positive integer of the form (2^(2^n))+1
multiply this by a number A, which is greater than the square root of P and is a primitive root modulo P (i.e., it is not a quadratic residue). Then take
Fermat_number
Prime number of the form 2^n – 1
21/2(p+1) is a square root of 2 mod q. By quadratic reciprocity, every prime modulus in which the number 2 has a square root is congruent to ±1 (mod
Mersenne_prime
Arithmetic procedure of verifying operations using modulo characteristics of digit 9
number is called the "digital root" of the original. If a number is divisible by 9, its digital root is 9. Otherwise, its digital root is the remainder it
Casting_out_nines
Number used for counting
Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related Meertens Other
Natural_number
Number that remains the same when its digits are reversed
number whose cube is a palindrome is 2201, and it is a conjecture the fourth root of all the palindrome fourth powers are a palindrome with 100000...000001
Palindromic_number
Class of natural numbers with many divisors
Ramanujan (1915). For example, the number with the most divisors per square root of the number itself is 12; this can be demonstrated using some highly composites
Superior highly composite number
Superior_highly_composite_number
Type of figurate number
Like a triangular number, the digital root in base 10 of a hexagonal number can only be 1, 3, 6, or 9. The digital root pattern, repeating every nine
Hexagonal_number
Symbols used to write numbers
make use of the representation of a number as a sequence of digits. The digital root is the single-digit number obtained by summing the digits of a given
Numerical_digit
Two raised to an integer power
Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related Meertens Other
Power_of_two
Multiplication table in Indian mathematics
typical 9 × 9 multiplication table where the entry in each cell is the digital root of the product of the column and row headings – in other words, each
Vedic_square
Numbers that evenly divide powers of 60
roots, such as how the Babylonians found an approximation to the square root of 2, perhaps using regular number approximations of fractions such as 17/12
Regular_number
Topics referred to by the same term
Look up root or roots in Wiktionary, the free dictionary. A root is the part of a plant, generally underground, that anchors the plant body, and absorbs
Root_(disambiguation)
Concept in number theory
In number theory, a narcissistic number (also known as a pluperfect digital invariant (PPDI), an Armstrong number (after Michael F. Armstrong) or a plus
Narcissistic_number
Natural number
perfect number. It is also the only perfect number that doesn't have a digital root of 1. 6 is the first unitary perfect number, since it is the sum of its
6
Integer whose multiples are digit rotations
specifically, this sequence is the set of primes p such that b is a primitive root modulo p. A conjecture of Emil Artin is that this sequence contains 37.395
Cyclic_number
Base-dependent property of integers
Meertens number Narcissistic number Perfect digit-to-digit invariant Perfect digital invariant Sum-product number Iannucci (2000) D. R. Kaprekar (1980–1981)
Kaprekar_number
Polyhedral number representing a tetrahedron
4.[dubious – discuss] By analogy with the cube root of x, one can define the (real) tetrahedral root of x as the number n such that Ten = x: n = 3 x
Tetrahedral_number
Modification of Android devices to gain rooted access
Rooting is the process by which users of Android devices can attain privileged control (known as root access) over various subsystems of the device, usually
Rooting_(Android)
Numbers that contain only the digit 1
prime, and this n {\displaystyle n} value is r {\displaystyle r} itself or a root of r {\displaystyle r} ) b {\displaystyle b} is not in the form − 4 k 4 {\displaystyle
Repunit
Integer divisible by sum of its digits
one as follows: Inserting zeroes into N will not change the sequence of digital sums (just as 21, 201 and 2001 are all 10-harshad numbers). If we insert
Harshad_number
Type of figurate number constructed by combining heptagons
numbers follows the pattern odd-odd-even-even. Like square numbers, the digital root in base 10 of a heptagonal number can only be 1, 4, 7 or 9. Five times
Heptagonal_number
Number whose square ends in the same digits
root in roots: for i in range(0, base): new_i = i * base ** (power - 1) + root new_root = polynomial_function(new_i) % pow(base, power) if new_root ==
Automorphic_number
American musician (born 1971)
main Rockerverb setup, Root began using a Neural DSP Quad Cortex in 2024, despite previously saying he would never use digital amplifier modelers. Atomic
Jim_Root
Function whose domain is the positive integers
\end{cases}}} See Multiplicative group of integers modulo n and Primitive root modulo n. 2 ω ( n ) ≤ d ( n ) ≤ 2 Ω ( n ) . {\displaystyle 2^{\omega (n)}\leq
Arithmetic_function
Topics referred to by the same term
84001 in base 10 the digit sum would be 8 + 4 + 0 + 0 + 1 = 13. The digital root - repeatedly apply the digit sum operation to the representation of a
Digital_sum
Numbers whose prime factors all divide the number more than once
powerful numbers in the interval [1,x]. Then k(x) is proportional to the square root of x. More precisely, c x 1 / 2 − 3 x 1 / 3 ≤ k ( x ) ≤ c x 1 / 2 , c = ζ
Powerful_number
Integer that is both a perfect square and a triangular number
all integers from 1 {\displaystyle 1} to n {\displaystyle n} has a square root that is an integer. There are infinitely many square triangular numbers;
Square_triangular_number
Centered figurate number
10333, 10837, 11353, and 11881. (sequence A003154 in the OEIS) The digital root of a star number is always 1 or 4, and progresses in the sequence 1,
Star_number
Three raised to an integer power
which is a power of two and much smaller. Power of 10 Power of two Square root of 3 Ranucci, Ernest R. (December 1968), "Tantalizing ternary", The Arithmetic
Power_of_three
Number used to approximate the square root of 2
comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins 1/1, 3/2, 7/5, 17/12
Pell_number
Sequence in number theory
one of his puzzles, Root Extraction, where a professor in retirement at Colney Hatch postulates this as a general method for root extraction. Let n {\displaystyle
Dudeney_number
Property of a number
is its digital root. Put another way, a number's additive persistence counts how many times we must sum its digits to arrive at its digital root. The additive
Persistence_of_a_number
Composite number which passes Miller–Rabin primality test
roots than +1 and −1, but if the modulus is composite, 1 can have square root +1 modulo some factors and −1 modulo others, leading to additional possibilities
Strong_pseudoprime
Number that can be used to count certain kinds of binary trees
with n nodes in which the root has degree zero or one and all other nodes have at most two children. Trees in which the root has at most one child are
Wedderburn–Etherington_number
Sequence of integers
= 0. {\displaystyle x^{3}-x-1=0.\,} This equation has 3 roots; one real root p (known as the plastic ratio) and two complex conjugate roots q and r. Given
Padovan_sequence
Natural number
smallest natural number that takes more than two iterations to compute its digital root as a repeated digit sum: 199 ↦ 1 + 9 + 9 = 19 ↦ 1 + 9 = 10 ↦ 1 + 0 =
199_(number)
Number in the 5th cell of any row of Pascal's triangle
x, to test whether it is a pentatope number we can compute the positive root using Ferrari's method: n = 5 + 4 24 x + 1 − 3 2 . {\displaystyle n={\frac
Pentatope_number
2009 video game
three to five with the total of their bracelet's number with the same digital root as marked on the door can pass through. Junpei escapes a flooding cabin
999: Nine Hours, Nine Persons, Nine Doors
999:_Nine_Hours,_Nine_Persons,_Nine_Doors
Power of a prime number
Every prime power excluding powers of 2 greater than 4 has a primitive root; thus the multiplicative group of integers modulo pn (that is, the group
Prime_power
Number in combinatorics
parenthesized sequence, and the internal nodes of the tree other than the root correspond to parenthesized groups. The parenthesized sequence itself may
Schröder–Hipparchus_number
Integer whose representation contains every digit in its number base
square numbers. No pandigital cube and no pandigital number with an integer root of higher degree are known. Only three pandigital numbers have prime factorizations
Pandigital_number
Number of orderings allowing ties
considered by Cayley, each root-to-leaf path has the same length, and the number of nodes at distance i {\displaystyle i} from the root must be strictly smaller
Ordered_Bell_number
Number sequence 3,0,2,3,2,5,5,7,10,...
x − 1 = 0 {\displaystyle x^{3}-x-1=0} . If the three solutions are real root α {\displaystyle \alpha } (with approximate value 1.324718 and known
Perrin_number
Munchausen number
Kaprekar's constant Kaprekar number Meertens number Narcissistic number Perfect digital invariant Sum-product number van Berkel, Daan (2009). "On a curious property
Perfect digit-to-digit invariant
Perfect_digit-to-digit_invariant
Product of two distinct primes ≡ 3 (mod 4)
exactly one of which is also in Qn The unique square root of a in Qn is called the principal square root of a modulo n The function f : Qn → Qn defined by
Blum_integer
Triangular array of natural numbers
word can be represented as a rooted tree. We start with a single node – the root node. This is initially the active node. Reading the word from left to right
Narayana_number
Number equal to the product of the sum and product of its digits
Meertens number Narcissistic number Perfect digit-to-digit invariant Perfect digital invariant Sloane, N. J. A. (ed.). "Sequence A038369 (Numbers n such that
Sum-product_number
Number that is the sum of the factorials of its digits
Meertens number Narcissistic number Perfect digit-to-digit invariant Perfect digital invariant Sum-product number Sloane, Neil, "A014080", On-Line Encyclopedia
Factorion
English television personality (born 2001)
split". Digital Spy. 4 October 2023. Retrieved 16 January 2025. "Love Island winner Sammy Root talks dating again following Jess Harding split". Digital Spy
Sammy_Root
Additive persistence Digital root Digit product dynamics Multiplicative digital root Multiplicative persistence Lychrel number Perfect digital invariant Happy
List_of_number_theory_topics
American insurance company
Root Insurance Company is an online car insurance company operating in the United States. Root Insurance headquarters are in Columbus, Ohio. Root is focused
Root,_Inc.
Positive integer with large prime factors
D. Naccache and I. E. Shparlinski, pp. 115–173 in Algebraic Aspects of Digital Communications, eds. Tanush Shaska and Engjell Hasimaj, IOS Press, 2009
Rough_number
Number that is the sum of its own digits, each raised to a given power
In number theory, a perfect digital invariant (PDI) is a number in a given number base ( b {\displaystyle b} ) that is the sum of its own digits each
Perfect_digital_invariant
Inverse function to a tower of powers
must replace the number by the sum of its digits before reaching its digital root, is O ( log ∗ n ) {\displaystyle O(\log ^{*}n)} . In computational
Iterated_logarithm
Natural number
prime 65,539 = the 6544th prime number, and both 6544 and 65539 have digital root of 1; a regular prime; a larger member of a twin prime pair; a smaller
60,000
Square root of the mean square
In mathematics, the root mean square (abbrev. RMS, rms or rms) of a set of values is the square root of the set's mean square. Given a set x i {\displaystyle
Root_mean_square
Operating as Dog Beach, LLC, a shell company subsidiary of Identity Digital "IANA — Root Zone Database". iana.org. Retrieved 31 May 2020. "IANA's list of
List of Internet top-level domains
List_of_Internet_top-level_domains
Arithmetic operation, inverse of nth power
number x of which the root is taken is the radicand. A root of degree 2 is called a square root and a root of degree 3, a cube root. Roots of higher degree
Nth_root
Algorithms for calculating square roots
Square root algorithms compute the non-negative square root S {\displaystyle {\sqrt {S}}} of a positive real number S {\displaystyle S} . Since all square
Square_root_algorithms
Data proving ownership of a public key
are called root programs. The most influential root programs are:[citation needed] Microsoft Root Program Apple Root Program Mozilla Root Program Oracle
Public_key_certificate
the note. The remaining 11 characters are numbers which, when their digital root is calculated, give a checksum also particular to that country. The W
Euro_banknotes
2016 video game
series shipments and digital sales had surpassed 500,000 units. Geraint Evans, the head of marketing of PQube, called their Root Letter sales "phenomenal"
Root_Letter
Certificate identifying a root authority
and computer security, a root certificate is a public key certificate that identifies a root certificate authority (CA). Root certificates are self-signed
Root_certificate
App to root an Android device
for all devices. Digital Trends said that using an app is "one of the easiest ways to root your Android device", and included KingoRoot in its list of most
Kingo_Root
Number that is its own Gödel number
Kaprekar number Narcissistic number Perfect digit-to-digit invariant Perfect digital invariant Sum-product number Richard S. Bird (1998). "Meertens number"
Meertens_number
Species of flowering plant in the celery family Apiaceae cultivated as an herb
similar, but is often preferred by chefs because it has a stronger flavor. Root parsley is very common in central, eastern, and southern European cuisines
Parsley
American engineering, procurement and construction company
KBR, Inc. (formerly Kellogg Brown & Root) is a U.S. based company operating in fields of science, technology and engineering. KBR works in various markets
KBR,_Inc.
2016 visual novel video game
from those two games included in the soundtrack. He also had the songs "Digital Root" and "Trepidation", which had been used in both previous games, be included
Zero_Time_Dilemma
2026 American film
Claes Bang, Temuera Morrison, Jacob Batalon, Frankie Adams, Miyavi, Stephen Root, and Morena Baccarin. Private investigator Walter Hale is killed in an apparent
The_Wrecking_Crew_(2026_film)
Stability criterion in control theory
computer to compute root loci, called a "Spirule" (after "spiral" and "slide rule"); it found wide use before the advent of digital computers. If a pole
Root_locus_analysis
Musical artist
genre's founding labels, DMZ. Loefah started off collaborating with the Digital Mystikz on the DMZ nights run in Brixton and was part of Mary Anne Hobbs'
Loefah
ISO standard unique string identifier for a digital object
A digital object identifier (DOI) is a persistent identifier, or persistent handle, used to uniquely identify various objects, standardized by the International
Digital_object_identifier
Root beer flavored soft drink
Hires Root Beer is an American brand of root beer that was most recently manufactured by Keurig Dr Pepper. Introduced in 1876, it was one of the longest
Hires_Root_Beer
Logarithmic unit expressing the ratio of physical quantities
root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio of 101/10 (approximately 1.26) or root-power
Decibel
Decimal representation of a number whose digits are periodic
Fermat's little theorem, which states that 10p−1 ≡ 1 (mod p). The base-10 digital root of the repetend of the reciprocal of any prime number greater than 5
Repeating_decimal
Method of identifying the fundamental causes of faults or problems
science and reliability engineering, root-cause analysis (RCA) is a method of problem solving used for identifying the root causes of faults or problems. It
Root-cause_analysis
2010 studio album by Les Savy Fav
Root for Ruin is Les Savy Fav's fifth studio album. Its scheduled release date was September 14, 2010, but after the album leaked in late July it was given
Root_for_Ruin
BBC executive
Jane Marianna Root (born 18 May 1957) is an executive in the media industry. She was controller of BBC Two from 1999 to 2004, and the first woman to serve
Jane_Root
Loaned translation of an expression
or phrase borrowed from another language by literal word-for-word or root-for-root translation. When used as a verb, "to calque" means to borrow a word
Calque
Town in County Carlow, Ireland
mathematical properties (any multiple of nine will have nine as its digital root), and was chosen because the town commission has nine members. Bagenalstown's
Bagenalstown
Term in music
The root position of a chord is the voicing of a triad, seventh chord, or ninth chord in which the root of the chord is the bass note and the other chord
Root_position
American actress (born 1964)
in the musical series Glee. Rosemont is married to fellow actor Stephen Root; the couple appeared on-screen together in a fourth-season episode of Fringe
Romy_Rosemont
Procedure to disinfect and fortify the interior of a tooth
Root canal treatment (also known as endodontic therapy, endodontic treatment, or root canal therapy) is a treatment sequence for the infected pulp of
Root_canal_treatment
American ambient musician
musician from the United States. He co-founded the drone and ambient label Root Strata. Cantu-Ledesma was born and raised in Texas, United States, and studied
Jefre_Cantu-Ledesma
Photography with a digital camera
linear resolution is the square root of the increase in area resolution (i.e., megapixels in the entire image). Both digital and film practical imaging systems
Digital_photography
Linear filter in the time domain
In signal processing, a root-raised-cosine filter (RRC), sometimes known as square-root-raised-cosine filter (SRRC), is frequently used as the transmit
Root-raised-cosine_filter
DIGITAL ROOT
DIGITAL ROOT
Surname or Lastname
English
English : patronymic from Root 1.
Girl/Female
Tamil
Divine power
Girl/Female
Indian
Light
Girl/Female
Tamil
Indukala | இஂதà¯à®•à®²à®¾
Digit of the Moon
Indukala | இஂதà¯à®•à®²à®¾
Girl/Female
Hindu, Indian
Giving Honour; A Digit of the Moon
Boy/Male
Indian, Punjabi, Sikh
Protector of All Directions
Girl/Female
Hindu
Digit of the Moon
Girl/Female
Hindu, Indian, Tamil
Light; Chamak
Girl/Female
Gujarati, Hindu, Indian
Expert; Splendor; Name of Parvati
Girl/Female
Indian
The right path
Surname or Lastname
English
English : affectionate nickname or term of address, from Middle English deinteth ‘pleasure’, ‘tidbit’ (Old French deintiet, from Latin dignitas ‘worth’, ‘value’). The word was also used as an adjective in the later form deinte (Old French deint(i)é) in the sense ‘fine’, ‘handsome’, ‘pleasant’.
Surname or Lastname
English
English : variant of Roots.
Surname or Lastname
English
English : nickname for a cheerful person, from Middle English rote ‘glad’ (Old English rÅt).English : metonymic occupational name for a player on the rote, an early medieval stringed instrument (Middle English, Old French rote, of uncertain origin but apparently ultimately akin to Welsh crwth).Dutch : topographic name for someone who lived by a retting place (Dutch root, a derivative of ro(o)ten ‘to ret’, akin to modern English rot), a place where flax is soaked in tubs of water until the stems rot to release the linen fibers.
Boy/Male
Indian, Sanskrit
Inflamed
Boy/Male
Indian, Sanskrit
Digit of the Moon
Girl/Female
Indian
Divine power
Girl/Female
Bengali, Gujarati, Hindu, Indian, Malayalam, Sanskrit
Progressive; A Digit of the Moon
Boy/Male
Indian, Sanskrit
Regent of a Direction
Girl/Female
Tamil
Dixita | திகà¯à®·à®¿à®¤
The right path
Dixita | திகà¯à®·à®¿à®¤
Girl/Female
Indian
Moon Rays
DIGITAL ROOT
DIGITAL ROOT
Boy/Male
Arabic, Turkish
Light of the Religion
Male
Icelandic
Icelandic form of Old Norse Ãvarr, ÃVAR means "bow warrior."Â
Boy/Male
Welsh
Legendary son of Alar.
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Moon
Surname or Lastname
English
English : variant spelling of Lemon.
Boy/Male
German
Brave as a Bear
Boy/Male
Scottish
Derived from the name Gilbride, meaning 'servant of St. Bridget'.
Boy/Male
Teutonic
Bold for his people.
Female
English
Pet form of English Mary, MOLLY means "obstinacy, rebelliousness" or "their rebellion."Â
Boy/Male
Hindu
The Lord of the Geeta
DIGITAL ROOT
DIGITAL ROOT
DIGITAL ROOT
DIGITAL ROOT
DIGITAL ROOT
a.
Of or performance to the fingers, or to digits; done with the fingers; as, digital compression; digital examination.
n.
Any plant of the genus Digitalis. The common English foxglove (Digitalis purpurea) is a handsome perennial or biennial plant, whose leaves are used as a powerful medicine, both as a sedative and diuretic. See Digitalis.
a.
Having leaflets like fingers; digitate.
n.
An animal having only two digits.
v. t.
To point out as with the finger.
n.
Any one of several extracts of foxglove (Digitalis), as the "French extract," the "German extract," etc., which differ among themselves in composition and properties.
n.
A little finger or toe, or something resembling one.
a.
Remote from the point of attachment or origin; as, the distal end of a bone or muscle
n.
A supposedly distinct vegetable principle as the essential ingredient of the extracts. It is a white, crystalline substance, and is regarded as a glucoside.
adv.
Toward a distal part; on the distal side of; distally.
n.
One twelfth part of the diameter of the sun or moon; -- a term used to express the quantity of an eclipse; as, an eclipse of eight digits is one which hides two thirds of the diameter of the disk.
a.
Pertaining to that which is distal; as, the distal tuberosities of a bone.
a.
Having five digits to the hand or foot.
a.
Alt. of Digitated
n.
A genus of plants including the foxglove.
n.
One of the digital bones of the hand or foot, beyond the metacarpus or metatarsus; an internode.
n.
The dried leaves of the purple foxglove (Digitalis purpurea), used in heart disease, disturbance of the circulation, etc.
n.
The distal tendon of a muscle.
a.
Having only two digits; two-toed.
adv.
Toward a distal part.