New posts in Elementary Number Theory

$3 \times 3$ matrix with determinant a large power of $2$

What are all possible positive integers $k$ such that $k=\frac{a^2+b^2+c^2}{bc+ca+ab}$ for some positive integers $a$, $b$, and $c$?

Why is $ \frac{5}{64}((161+72\sqrt{5})^{-n}+(161+72\sqrt{5})^{n}-2)$ always a perfect square?

Primes Powers and Mods

Prove that $\frac{(3 a+3 b) !(2 a) !(3 b) !(2 b) !}{(2 a+3 b) !(a+2 b) !(a+b) ! a !(b !)^{2}}$ is an integer.

What happens when we (incorrectly) make improper fractions proper again?

Does $\Phi_n(\alpha)=0$ in $\Bbb{F}_p$ for some $\alpha\in\mathbb{F}_p$ imply that $\mathrm{ord}_p(\alpha) = n$?

An Interesting Question I Posed to Myself About $\pi$ as an Average.

Solve the following equation in integers $x,y:$ $x^2+6xy+8y^2+3x+6y=2.$

If positive integers $a$, $b$, $c$ satisfy $\frac1{a^2}+\frac1{b^2}=\frac1{c^2}$, then the sum of all values of $a\leq 100$ is ...