List questions from infinite-descent | MathQA

No positive integers $(a,b)$ satisfying $2^b -1\mid 2^a +1$ (AoPS Vol 2)

Published on 25 Mar 2026 - 9:38

Show that there are infinitely many solutions $x, y, z \in\mathbb N$ of the following equation $x^2 + y^3 = z^7.$

Published on 25 Mar 2026 - 9:43

How does this geometric application of proof by infinite descent work

Published on 25 Mar 2026 - 9:37

Solutions in $\mathbb{Z}$ for $x + y = xy$ : Proof by infinite descent

Published on 25 Mar 2026 - 9:37

Proof Completion: Solutions in $\mathbb{Z}$ for $x + y = xy$

Published on 25 Mar 2026 - 9:35

There are no positive integers such that $a+b^2$, $a^2+b$ are both powers of $5$

Published on 25 Mar 2026 - 9:43