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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...

   In modular arithmetic, the integers coprime (relatively prime) to n from the set {,, …,} of n non-negative integers form a group under multiplication modulo n, called the multiplicative group of integers modulo n.

4. Modular multiplicative inverse - Wikipedia

   en.wikipedia.org/wiki/Modular_multiplicative_inverse

   Modular multiplicative inverses are used to obtain a solution of a system of linear congruences that is guaranteed by the Chinese Remainder Theorem. For example, the system X ≡ 4 (mod 5) X ≡ 4 (mod 7) X ≡ 6 (mod 11) has common solutions since 5,7 and 11 are pairwise coprime. A solution is given by

5. Field (mathematics) - Wikipedia

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

   The genus can be read off the field of meromorphic functions on the surface. Functions on a suitable topological space X into a field F can be added and multiplied pointwise, e.g., the product of two functions is defined by the product of their values within the domain: (f ⋅ g)(x) = f(x) ⋅ g(x). This makes these functions a F-commutative ...

6. 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.

7. 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.