5 problems

Stronger linear lower-bound conjecture. For each prime $k>3119$,

For positive integers $h$ and $k$, define … where $\lfloor x\rfloor$ is the greatest integer less than or equal to $x$, and define … Let $C_1$ and $C_2$ be any fixed positive numbe…

Linear lower-bound conjecture. For each prime $k>233$,

Positivity conjecture. For each odd prime $k>5$,

General arithmetic-sum conjecture. If