Proof by induction that $5|11^n-6$ for all positive integers $n$ 
Prove by induction that $5|11^n-6$ for all positive integers $n$

Let $p(n) = 11^n-6.$ We have $p(1) = 5$, thus it holds for $p(1)$. Assume it holds for $p(k)$. We will prove that it's true for $p(k+1)$. We have $p(k+1) = 11^{k+1}-6$. But $6 = 11^k-f(k).$ Thus
$$f(k+1) = 11\cdot 11^k-11^k+f(k) = 10\cdot 11^k+f(k). $$
$5|(10\cdot 11^k+f(k))$ by hypothesis thus the statement is true for $p(k+1)$. Hence it's true for $p(n)$. 
Is the above correct?

Let $x=11^n-6$ then $$11^{n+1}-6=11(x+6)-6=11x+60$$ and this later is divisible by $5$ if $x$ is.
