What is the largest prime factor of $55^{100}+55^{101}+55^{102}$

Question

Can anyone help me on this?

What is the largest prime factor of $55^{100}+55^{101}+55^{102}$?

I know $55^{100}+55^{101}+55^{102}=55^{100}*(1+55+55^2)$, but I don't know how to move forward from here.

Answer 1

$1+55+55^2 = 3081 = 3 \cdot 13 \cdot 79$.

Answer 2

You can factor out $55^{100}$ from the expression. The largest prime factor of that number is $11$.

Then it remains to factor $1+55+55^2$, which Prof. Israel did in his answer.