2 problems

For integers $t\geq 3$, define … The numerical evidence suggests that $f_3=0$ and $f_t>0$ for $t\geq 4$. Positivity conjecture. For integers $t\geq 4$, $f_t>0$. On the other hand,…

Let $r=2d$ with $1\leq d\leq 50$, let $p\geq 5$ be prime, and consider the equation … Here $d,x,z$ are integers. Alternating-cube perfect-power conjecture. The possible integer sol…