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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. Legendre symbol - Wikipedia

   en.wikipedia.org/wiki/Legendre_symbol

   In number theory, the Legendre symbol is a multiplicative function with values 1, −1, 0 that is a quadratic character modulo of an odd prime number p: its value at a (nonzero) quadratic residue mod p is 1 and at a non-quadratic residue (non-residue) is −1.

4. Modular equation - Wikipedia

   en.wikipedia.org/wiki/Modular_equation

   In that sense a modular equation becomes the equation of a modular curve. Such equations first arose in the theory of multiplication of elliptic functions (geometrically, the n 2 -fold covering map from a 2- torus to itself given by the mapping x → n · x on the underlying group) expressed in terms of complex analysis .

5. Residue number system - Wikipedia

   en.wikipedia.org/wiki/Residue_number_system

   A residue numeral system (RNS) is a numeral system representing integers by their values modulo several pairwise coprime integers called the moduli. This representation is allowed by the Chinese remainder theorem, which asserts that, if M is the product of the moduli, there is, in an interval of length M, exactly one integer having any given set of modular values.

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. Fermat's little theorem - Wikipedia

   en.wikipedia.org/wiki/Fermat's_little_theorem

   This is widely used in modular arithmetic, because this allows reducing modular exponentiation with large exponents to exponents smaller than n. Euler's theorem is used with n not prime in public-key cryptography , specifically in the RSA cryptosystem , typically in the following way: [ 10 ] if y = x e ( mod n ) , {\displaystyle y=x^{e}{\pmod ...