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 Jan 29 comment Solve $z^4+2z^3+3z^2+2z+1 =0$ @DylanSp it is the discriminant $b^2-4ac$ from the quadratic equation. Jan 27 comment Some hints for “If a prime $p = n^2+5$, then $p\equiv 1\mod 10$ or $p\equiv 9\mod 10$” Think about $n^2+5\pmod2$ and $n^2+5\pmod5$. I think this will help. Jan 15 comment Suprema and infima in real numbers Don't forget that squaring real numbers will make them nonnegative, so $-\infty$ is not an infimum for any of the above. Jan 11 comment How to prove $cn < n^{\log_{2}n}$ Maybe you mean to write: for any given (but fixed!) $c$, there exists $N$ such that for all $n>N$, we have the inequality. Jan 6 awarded Popular Question Jan 5 comment what is the maximum area of a cyclic pentagon? Have you put any thought into this? Ideas, strategies, etc.? If so, what has come to mind? Jan 1 comment Prove that $\frac{(a-b)^2}{8a} \le \frac{a+b}{2} - \sqrt{ab} < \frac{(a-b)^2}{8b}$ when $00$. Dec 10 comment How do you factor $x^2-x-1$? Quadratic formula gives the roots, which is all you need to factor quadratic equations. Dec 8 comment Can the existence of infinitely many even perfect numbers be settled by a diagonal argument? I'm not sure about all of the subtleties of language differences, but I think it should actually be Euclidean @barak manos. If it is generally spelled with an 'i' in your country's English, my apologies. :-) +$1$ for the question Dec 4 comment Sylow Subgroups small question - -shared elements of the $p$-subgroups Nice hint: +$1$. Dec 4 revised how to prove this type of problems? added 27 characters in body Dec 4 comment Explain proof by contradiction. @5xum: I suppose it's subjective in that manner. I don't deny the connection between the statement and its contrapositive (but then again, one should see a connection among all the standard types of proof), but I would consider anything that results in a contradiction a proof by contradiction... Also, Graham Kemp's answer is identical to mine, except more succinct.