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

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.

• @SathasivamK That's neither largest nor prime. Sep 22 '16 at 18:08
• @robert Israel you're right Sep 22 '16 at 18:13
• The answer is 79 Sep 22 '16 at 18:15

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