Mod Question

Show that 5^n + 6^n = 0 mod 11, for all odd number n

My initial attempt was to prove by induction. Base case is obvious, and the induction step would be to prove for n + 2.

I'm trying to play around by writing in the mod definition but no luck so far. Any advice?

Quote:

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Originally Posted by hashshashin715

Show that 5^n + 6^n = 0 mod 11, for all odd number n

My initial attempt was to prove by induction. Base case is obvious, and the induction step would be to prove for n + 2.

I'm trying to play around by writing in the mod definition but no luck so far. Any advice?

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You want to show that IF

is divisible by 11

THEN



will also be divisible by 11.

So

Thanks a lot, i got it now.

I was getting stuck at the part where we have (25)5^k + (36)5^k. Breaking them down like that was clever.