# Proof: Uniqueness of multiplicative inverse

Prove that any multiplicative inverse i of m modulo n is unique modulo n.

## Proof #

Let i and j be two multiplicative inverses of m modulo n:

We ought never to allow ourselves to be persuaded of the truth of anything unless on the evidence of our own reason– René Descartes

Prove that any multiplicative inverse i of m modulo n is unique modulo n.

Let i and j be two multiplicative inverses of m modulo n: