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Math Help - Reducing a congruence

  1. #1
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    Reducing a congruence

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

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