2 problems

Exponential-sum and small-order conjecture. There exists a non-increasing mapping $f:\mathbb{N}\to\mathbb{R}_+$ such that:

For an integer $a$ and a positive integer $r$, define … where $\operatorname{ord}_p(a)$ is the multiplicative order of $a$ modulo the prime $p$. Erdős's conjecture. For every…