# Math Help - Reducing a congruence

1. ## Reducing a congruence

If $x^6 \equiv y^6 \mod{7^6}$, does this imply $x\equiv y \mod{7}$?

2. Originally Posted by mathman88
If $x^6 \equiv y^6 \mod{7^6}$, does this imply $x\equiv y \mod{7}$?

Of course not: $(-1)^6=1^6\!\!\!\pmod{7^6}\,,\,\,but\,\,\,-1\neq 1\!\!\!\pmod 7$

Tonio