New posts in diophantine-equations

diophantine equations $x^3-2y^3=1$

Show $1+x+(x^2/2!)+ \cdots + (x^n/n!)=0$ has no rational solutions for all $n>1$.

Solutions to the diophantine equation $x^3+y^3+z^3+w^3=1$

Integer solutions of $m^2+(m+1)^2=n^4+(n+1)^4$

Problem Heron of Alexandria.

How to find a "better description" (e.g. recurrence relation) for this sequence?

Coefficients in expansion of $(\sqrt[3]{2} - 1)^m$

Find all solutions of the equation $n^m=x^2+py^2$ which satisfy the following properties

Diophantine equation. Three.

Solve Diophantine equation with three variables part two

A Diophantine equation involving factorial

Diophantine vs. existential definability

Prove that $(2^n-1)(3^n-1)$ is not a perfect square

On the diophantine equation $x^{m-1}(x+1)=y^{n-1}(y+1)$ with $x>y$, over integers greater or equal than two

prove Diophantine equation has no solution $\prod_{i=1}^{2014}(x+i)=\prod_{i=1}^{4028}(y+i)$

Does Diophantine equation $1+n+n^2+\dots+n^k=2m^2$ have a solution for $n,k \geq 2$?

How many integer pairs satisfy the ellipse $x^2+ay^2=r?$

Integer solutions for $\frac{1}{x^2}+\frac{1}{y^2}=\frac{1}{z^2}$?

On elementary proofs of Fermat's Last Theorem

A 3rd grade math problem: fill in blanks with numbers to obtain a valid equation