Question 22
Let $n$ be a positive integer.
Prove that $a(n) = n^5 + 5^n$ is divisible by $11$ if and only if $b(n) = n^5 \cdot 5^n + 1$ is divisible by $11$.
Prove that $a(n) = n^5 + 5^n$ is divisible by $11$ if and only if $b(n) = n^5 \cdot 5^n + 1$ is divisible by $11$.