2 problems

Let $v_p$ denote the $p$-adic valuation. The variables $x$ and $q$ are integers with $x>1$, and $p$ and $q$ are primes in the second assertion. Sharp upper-bound conjecture for Fer…

For a prime $p>2$, write $q_2(p)=(2^{p-1}-1)/2$. Arithmetic progression nonvanishing conjecture. For every pair of positive integers $m>a>0$ with $\gcd(m,a)=1$, there are infinitel…