Question 1
Let $a$ and $b$ be relatively prime positive integers such that $(a, b) \ne (2, 1)$. Show that
$$
\text{rad}(a^n + b^n) \ne \text{rad}(a^m + b^m),
$$
for any distinct positive integers $m$ and $n$. Here $\text{rad}(c)$ denotes the distinct primes dividing the integer $c$.
$$
\text{rad}(a^n + b^n) \ne \text{rad}(a^m + b^m),
$$
for any distinct positive integers $m$ and $n$. Here $\text{rad}(c)$ denotes the distinct primes dividing the integer $c$.