New posts in Elementary Number Theory

Prime factoring $2^{22} + 1$ the sneaky way?

Addition and multiplication in terms of arrows in the poset category where an existing arrow means "divides".

Prove that if x,y,z are positive integers such that $x^3+y^3+z^3=3(x+y+z+xyz)$ then they must be consecutive numbers

Is the representation of any prime of the form $6n+1$ as $a^2+3b^2$ essentially unique?

Analyzing a Diophantine equation: $A^k + 1 = B!$ Efficient way to solve.

Number of $n \to p \bmod n$ before getting to 0

For any odd prime $p$, a quadratic is solvable mod $p^2$ if it is solvable mod $p$, and $p$ does not divide the discriminant and leading coefficient.

Prove that the diophantine equation $(xz+1)(yz+1)=az^{k}+1$ has infinitely many solutions in positive integers.

Starting with $1,9,9,3$ the sequence continues as the last digit of the sum of preceding 4 terms. Will subsequence $7, 3, 6, 7$ ever appear in it?

Proving that $\left[ \mathbb{Q} \left( \sqrt[3]{4+\sqrt{5}} \right ) : \mathbb{Q} \right] = 6$