<s>[INST] Prime Factorization of $15^8 + 16$ I have created a problem and I am not able to find the answer. What is the prime factorization of $15^8 + 16$? The thing is I can find an answer with a calculator easily, but what is the step by step approach to the problem.
 [/INST] \begin{align*}
  n^8+n+1 &= (n^2+n+1)(n^6-n^5+n^3-n^2+1) \\
  15^8+15+1 &= (15^2+15+1)(15^6-15^5+15^3-15^2+1) \\
  &= 241 \times 10634401  \\
\end{align*}
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