How to find the inverse of a unit in a polynomial quotient ring. Notice that $x^3+1$ is actually reducible, and hence the quotient is actually not an integral domain. However, $1+x^2$ is relatively prime to $x^3+1$ and hence has an inverse in the quotient, by the euclidean algorithm.
Comparison test, proving divergence Nice answer but I think your last line should actually be the first thing you say. If $a_n$ does not converge to $0$ then both diverge. WLOG assume $a_n$ converges to $0$. Then we can use the limit comparison test...
Nov 11
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Proof using Fermat's Little Theorem Also notice $n^{10}$ is congruent to $1$ mod $11$ iff $11$ does not divide $n$. But if $11$ divides $n$ then the problem is even easier.
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