5 problems

Let $t$ be a positive integer. The equation … has the obvious positive integer solution $(x,y)=(1,1)$. The conjecture on nontriangular parameters. If $t$ is not of the form $u^2+u$…

Euler's infinitude conjecture. The equation

Integral-solutions conjecture. The equation

Let $n\geq 3$ and let $x_1,\ldots,x_n,y_1,\ldots,y_n$ be variables in the domain of the intended Diophantine equations. Conjecture. The simultaneous equations … have infinitely man…

Let $p>3$ be prime, let $\alpha(p)$ be the power-series solution of the quartic equation $(Eq)$ considered in the paper, and in the case $p\equiv 2\pmod 3$ set … Let…