1. ## mod questions

Show that 5^e +6^e is congruent 0 (mod 11) for all odd numbers e

Prove that 6(4^n) is congruent 6(mod 9) for any n>=0

2. $x^n + y^n = (x+y)(x^{n-1}-x^{n-2}y+x^{n-3}y^2-...)$ where $n$ is odd.

3. Originally Posted by ashe2203

Prove that 6(4^n) is congruent 6(mod 9) for any n>=0
for $n=0$, we have $6(4^0) \equiv 6\mod 9$
for for $n=1$, we have $6(4^1) \equiv 24\mod 9 \equiv 6\mod 9$
for suppose it is true that for $n=k$, $6(4^k) \equiv 6\mod 9$..
then, $6(4^{k+1}) = 6(4^k)(4) \equiv (6)(4)\mod 9 \equiv 24\mod 9 \equiv 6\mod 9$.. QED.
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