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Modular multiplicative inverse

In mathematics, particularly in the area of arithmetic, a modular multiplicative inverse of an integera is an integer x such that the product ax is congruent to 1 with respect to the modulus m. In the standard notation of modular arithmetic this congruence is written as ax≡1(modm),{\displaystyle ax\equiv 1{\pmod {m}},}which is the shorthand way of writing the statement that m divides (evenly) the quantity ax − 1, or, put another way, the remainder after dividing ax by the integer m is 1.

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