If n=rs, r>2 and s>2, gcd(r,s)=1, show ≡ 1 (mod n).
I really have no ideas -- something with Euler's Criterion maybe? -- any help would be appreciated. Thanks.
Note that here , and therefore .
Euler's Theorem implies that ; also is even since . Hence . In a similar way, we have the congruence .
By hypothesis , so we can merge the main congruences to one that is equivalent, namely . But , so .