# Math Help - Modulo Question: Proof

1. ## Modulo Question: Proof

Prove that there is no integer x satisfying ax 1(mod m) if a is a divisor of m and a is neither 1 nor m.

All i did:
ax= 1 + rm where r is integer
Then:
x=1/a +rm/a
dont know how to continue.

Any help will be appreciated.
Thanks in advance

2. Originally Posted by firebio
Prove that there is no integer x satisfying ax 1(mod m) if a is a divisor of m and a is neither 1 nor m.

All i did:
ax= 1 + rm where r is integer
Then:
x=1/a +rm/a
dont know how to continue.

Any help will be appreciated.
Thanks in advance

$a\mid m\Longrightarrow m=ab$ ; if we had $xa=1\!\!\!\pmod m$ , then we'd get $xa=1+km=1+akb\Longrightarrow a(x-kb)=1\Longrightarrow a=\pm 1$ , which is not the case by assumption.

Tonio