New posts in Diophantine Equations

When is $p^2+1$ twice of a prime?

How do you show that, for any integer, there is a triangle with side rational lengths and that integer area?

Are Transitions in a Hydrogen Atom Unique

Solutions to $a,\ b,\ c,\ \frac{a}{b}+\frac{b}{c}+\frac{c}{a},\ \frac{b}{a} + \frac{c}{b} + \frac{a}{c} \in \mathbb{Z}$

What is the smallest integer greater than 1 such that $\frac12$ of it is a perfect square and $\frac15$ of it is a perfect fifth power?

Find all pairs of positive integers $(a,b)$ such that $2^a+5^b$ is a perfect square.

Find the values of $p$ and $q$

Solving integer equation $a^3+b^3=a^2+72ab+b^2$

Integer solutions to $x^3=y^3+2y+1$?

If $ab \mid c(c^2-c+1)$ and $c^2+1 \mid a+b$ then prove that $\{a, b\}=\{c, c^2-c+1 \}$