How to prove that if: a + b + c == 0 (mod n)$ and a^5 + b^5 + c^5 == 0 (mod n), abc == 0 (mod n) ;/
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Not true! $\displaystyle 1+1+1\equiv 0 \mod 3$ $\displaystyle 1^5+1^5+1^5\equiv 0 \mod 3$ but $\displaystyle 1^3 \not\equiv 0 \mod 3$.
Originally Posted by mol How to prove that if: a + b + c == 0 (mod n)$ and a^5 + b^5 + c^5 == 0 (mod n), abc == 0 (mod n) ;/ This is false: take $\displaystyle a=b=c=2\,,\,\, n = 6$ Tonio
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