4 problems

Let $q$ and $n$ be positive integers, and let $p_1,\ldots,p_n$ be distinct integers relatively prime to $q$ such that $q>(7/4)^n$ and … Assume that for every $k\in\{1,\ldots,n\}$,…

Harshitha's conjectures. The limits satisfy

Let $t_n$ and $t_n'$ be the quantities defined earlier in the paper, and let $\left(\frac{\cdot}{p}\right)$ denote the Legendre symbol. The tangent permanent conjecture. (i) For ev…

Generalized positivity conjecture. The first sum is a polynomial in $1+\cos(x)$ with nonnegative integral coefficients, and the second satisfies