2 problems

Let $R$ be a commutative ring with identity. For a positive integer $s$, let $p_{2s}(R)$ denote the least number of $2s$-th powers needed in the relevant representation defining th…

Let $d\geq 3$ be an integer, let $\mathbbm{k}$ be a field of characteristic $0$ or greater than $d$, and let $r,s,n$ be positive integers. Consider an identity … where each…