Smallest Prime Divisor

Number Theory Level pending

What is the smallest prime divisor of $\large5^{{{{{6}^{7}}^{8}}^{9}}^{10}} +1$ ?

5 3 2 7

1 solution

Hana Wehbi
Nov 18, 2016

$5$ to any power is odd, so this number is even. Thus, $2$ is a prime divisor and it happens to be the smallest prime divisor.