Thread: 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

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

; if we had , then we'd get , which is not the case by assumption.

Tonio