New posts in Elementary Number Theory

Calculating $\phi(100)$ where $\phi$ is the totient function

Prove that $p | a_i$ for some i

Prove that $2^{n}+1$ is not a cube of an integer for all $n\in\mathbb{N}$

Prove that there are no integer solutions to $x\left(y^{2}-1\right)=y\left(2+\frac{1}{x}\right)$

Can a sum of $n$ squares be expressed as the sum of $n/2$ squares?

For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$

Olympiads Number Theory Problem: Show that there are no positive $a,b,c\in\Bbb Z$ such that $\frac{a^2+b^2+c^2}{3(ab+bc+ca)}\in\Bbb Z$

Is it possible that $2^{2A}+2^{2B}$ is a square number?

Any way to determine if a finite multiset of natural numbers can be combined via addition or subtraction to form zero?

Prove there is no rational number r such that $2^r = 3$