Concepts inThe modulo N extended GCD problem for polynomials
Greatest common divisor
In mathematics, the greatest common divisor (gcd), also known as the greatest common factor (gcf), or highest common factor (hcf), of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder. For example, the GCD of 8 and 12 is 4. This notion can be extended to polynomials, see greatest common divisor of two polynomials.
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Modular arithmetic
In mathematics, modular arithmetic (sometimes called clock arithmetic) is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value¿the modulus. The Swiss mathematician Leonhard Euler pioneered the modern approach to congruence in about 1750, when he explicitly introduced the idea of congruence modulo a number N. Modular arithmetic was further advanced by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.
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Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, x ¿ x/4 + 7 is a polynomial, but x ¿ 4/x + 7x is not, because its second term involves division by the variable x (4/x), and also because its third term contains an exponent that is not an integer (3/2).
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