Modulo is an operation that finds the remainder of an integer division. For example: $$ 16\hspace{0.25cm}modulo\hspace{0.25cm}6 = 4 $$ Because \(16 / 6 = 12 + 4\).

The modular multiplicative inverse (also called inverse modulo) of an integer \(a\hspace{0.25cm} mod\hspace{0.25cm}m\) is an integer \(x\) such that: $$ ax \equiv 1 (mod\hspace{0.25cm}m) $$ It should be noted that such an inverse only exists if \(a\) and \(m\) are coprime (meaning that their greatest common divisor is 1).

The modular multiplicative inverse is

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