Show that an inverse ofamodulomdoes not exist ifgcd(a, m) > 1.

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- Oct 18th 2008, 10:46 PMaaronrjInverse Modulus Proof
Show that an inverse of

*a***modulo***m*does not exist if**gcd**(*a, m*) > 1. - Oct 19th 2008, 12:54 AMMoo
Hello,

b is an inverse of a modulo m if

This means we have : where k is an integer. i.e.

By Bézout's identity, we know that :

it appears in the French wikipedia and I've been taught this, but I don't know where to find it in English (not in wikipedia nor in mathworld). If you want a proof, tell me.

And you're done.