# Thread: Prove divisibility

1. ## Prove divisibility

How to prove that if:
a + b + c == 0 (mod n)$and a^5 + b^5 + c^5 == 0 (mod n), abc == 0 (mod n) ;/ 2. Not true!$\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$. 3. Originally Posted by mol How to prove that if: a + b + c == 0 (mod n)$ 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