Question 69
a) Prove that $2^n + 3^n + 5^n + 8^n$ is not a perfect square for any positive integer $n$.
b) Find all positive integers $n$ so that $1^n + 4^n + 6^n + 7^n = 2^n + 3^n + 5^n + 8^n$.
b) Find all positive integers $n$ so that $1^n + 4^n + 6^n + 7^n = 2^n + 3^n + 5^n + 8^n$.