MathNet 2026 — Part 04 Question 111

Let $t$ a non-zero natural integer. Show that there is an integer $n\gt 1$ first with $t$ such as for any integer $k \geq 1$, the integer $n^{k}+t$ is not a power (i.e. it is not of the form $m^{r}$ with $m \geq 1$ and $r \geq 2$ ).