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2. Modular arithmetic - Wikipedia

   en.wikipedia.org/wiki/Modular_arithmetic

   In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae , published in 1801.

3. Multiplicative group of integers modulo n - Wikipedia

   en.wikipedia.org/wiki/Multiplicative_group_of...

   If n is composite, there exists a possibly proper subgroup of , called the "group of false witnesses", comprising the solutions of the equation =, the elements which, raised to the power n − 1, are congruent to 1 modulo n. [8]

4. Erdős–Straus conjecture - Wikipedia

   en.wikipedia.org/wiki/Erdős–Straus_conjecture

   For every , the equation = (+ +) is easily solvable modulo any prime, or prime power, but there appears to be no way to piece those solutions together to get a positive integer solution to the equation. Nevertheless, modular arithmetic, and identities based on modular arithmetic, have proven a very important tool in the study of the conjecture.

5. Modulo (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Modulo_(mathematics)

   Modulo is a mathematical jargon that was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. [3] Given the integers a, b and n, the expression "a ≡ b (mod n)", pronounced "a is congruent to b modulo n", means that a − b is an integer multiple of n, or equivalently, a and b both share the same remainder when divided by n.

6. Primitive root modulo n - Wikipedia

   en.wikipedia.org/wiki/Primitive_root_modulo_n

   In modular arithmetic, a number g is a primitive root modulo n if every number a coprime to n is congruent to a power of g modulo n. That is, g is a primitive root modulo n if for every integer a coprime to n, there is some integer k for which g k ≡ a (mod n). Such a value k is called the index or discrete logarithm of a to the base g modulo n.

7. Root of unity modulo n - Wikipedia

   en.wikipedia.org/wiki/Root_of_unity_modulo_n

   In number theory, a kth root of unity modulo n for positive integers k, n ≥ 2, is a root of unity in the ring of integers modulo n; that is, a solution x to the equation (or congruence) (). If k is the smallest such exponent for x, then x is called a primitive kth root of unity modulo n. [1]