Prove that 9^n-8^n is divisible by 8

It is not divisible by 8 ( leaves remainder 1)

write 9^n =(1+8)^n and expand it binomially , the soln will become clear!!

9^n-8^n is divisible by 8.

let n=1.1 is div by8

let n=k.and let 9^k-8^kis divisible by8.

if we can prove 9^k+1-8^k+1is divisible by8 ,it can b proved.

let 9^k-8^k=8m (from 3rd statement)

now,9^k+1-8^k+1=9^k-8^k +9-8=9^k-8^k+1

which is divisible by 8.

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