Show that $\frac{a_1}{b_1}+\frac{a_2}{b_2}+...+\frac{a_n}{b

Every sixth polynomial shares a factor of $(a^2-6)$

Localizations of an Artinian ring are isomorphic to quotients.

Does $\sum{\ln n\over n^{4/3}}$ converge or diverge?

Are there infinitely many natural numbers $n$ such that $\mu(n)=\mu(n+1)=\pm 1$?

how to simplify $ 2 \sqrt{2}\left(\sqrt{9-\sqrt{77}} \right) $

Value of $\sum 1/p^p$

An inequality using convex functions: If $\frac{a^2}{1+a^2}+\frac{b^2}{1+b^2}+\frac{c^2}{1+c^2} = 1$ then $abc \le \frac1{2\sqrt 2}$

Is the numerator of $\sum_{k=0}^n \frac{(-1)^k}{2k+1}\binom{n}{k}$ a power of $2$?

Prove that for every three non-zero integers, a,b and c, at least one of the three products ab,ac,bc is positive

Does $L^p$ have a basis for which the Pythagorean identity with exponent $p$ holds?

The series of reciprocals of the least common multiples of integers $X_1<X_2<\dots$ converges

Is there a way to extract the diagonal from a matrix with simple matrix operations

Show that $\frac{a_1}{b_1}+\frac{a_2}{b_2}+...+\frac{a_n}{b_n} \geq n$