Category
page 1Modular arithmetic
Fermat's little theorem
mathematical theorem that, for any prime 𝑝, the 𝑝th power of any integer 𝑛 is congruent to 𝑛 modulo 𝑝
modular arithmetic
system of algebraic operations defined for remainders under division by a fixed positive integer; system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus
Chinese remainder theorem
theorem for solving simultaneous congruences
Euler's totient function
function which gives the number of integers relatively prime to and not greater than its input
Wilson's theorem
necessary and sufficient condition for a number to be prime
Euler's theorem
generalization of Fermat's little theorem, that given coprime positive integers 𝑛 and 𝑎, then the φ(𝑛)-th power of 𝑎 is congruent to 1 modulo 𝑛, where φ is Euler’s totient function
Luhn algorithm
simple checksum formula
Legendre symbol
multiplicative function with values 1, −1, 0
modulo operation
In computing and mathematics, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, the latter being called the modulus of the operation.
quadratic reciprocity
theorem
congruence relation
equivalence relation in algebra
quadratic residue
integer that is a perfect square modulo some integer
discrete logarithm
problem of inverting exponentiation in finite groups
Carmichael number
composite number in number theory
Jacobi symbol
generalization of the Legendre symbol
primitive root modulo n
generator of the multiplicative group of integers modulo n
Fermat primality test
primality test
linear congruential generator
pseudorandom number generator
Carmichael function
arithmetic function
Euler's criterion
in number theory concerning primes
automorphic number
a natural number whose square "ends" in the same digits as the number itself
modular multiplicative inverse
element which, once multiplied by a given element, gives a congruent of one
modular exponentiation
type of exponentiation performed over a modulus
multiplicative order
mathematical function
Solovay–Strassen primality test
probabilistic primality test
Kronecker symbol
generalization of the Jacobi symbol to all integers
Hensel's lemma
theorem in commutative algebra
Gauss's lemma
Condition under which a integer is a quadratic residue
multiplicative group of integers modulo n
group of units of the ring of integers modulo n
Zeller's congruence
algorithm to calculate the day of the week in the Gregorian and Julian calendars
Pisano period
Period of the Fibonacci sequence modulo an integer
Vedic square
multiplication table in Indian mathematics
reduced residue system
set of φ(n) integers such that each integer is relatively prime to n and no two are congruent modulo n
Cubic reciprocity
conditions under which the congruence x3 equals p (mod q) is solvable
residue number system
arithmetic system
Congruence of squares
in number theory, a congruence commonly used in integer factorization algorithms
Thue's lemma
Lemma states that every modular integer may be represented by a "modular fraction"
Jordan's totient function
A function in mathematics, number theory
Barrett reduction
algorithm in modular arithmetic
Montgomery reduction
algorithm for fast modular multiplication
additive polynomial
polynomial that preserves addition