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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.

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    $\begingroup$ @SathasivamK That's neither largest nor prime. $\endgroup$ Sep 22 '16 at 18:08
  • $\begingroup$ @robert Israel you're right $\endgroup$ Sep 22 '16 at 18:13
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    $\begingroup$ The answer is 79 $\endgroup$ Sep 22 '16 at 18:15
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$1+55+55^2 = 3081 = 3 \cdot 13 \cdot 79$.

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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.

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