New posts in Diophantine Equations

Problem of Mary Somerville and Hypatia

Solve in $\mathbb{Z}$ the equation $x^4 + 1 = 2y^2$.

Is "$a^p + b^p = c^p + d^p \Rightarrow (a+b) \equiv (c+d) \mod p$" true?

Simple Method of Solution of $X^p+Y^p=(X+1)^p$

A diophantine equation with unknown exponents: $ 4^n + 5^n = 7^m + 2^m $

How to solve the pair of equations $4a-11b+12c=22$ and $a+5b-4c=17$ over the integers?

Solution of $X^5=5 Y (Y+1)+1$ in integers.

An elliptic curve $x(x - 78126^2)(x - 4\times5^7) = y^2$ for $x_1^7+x_2^7+\dots +x_8^7= x_9^7$

Equation with solution in prime numbers

Is there a formula for this specific pattern of Pythagorean Triangles sharing an area?