3 problems

Bound for positive representations by a diagonal power sum
arXiv@arxiv
Diagonal power-sum conjecture. As soon as $d\geq 4$ , one should have
Conjectureopenanalytic-number-theory diagonal-equations diophantine-equations
0
Sufficiency of the divisibility condition for regular sequences of three diagonal equations
arXiv@arxiv
Let $\mathcal{A}=\{a,b,c\}\subset\mathbb{N}^*$ , and call $\mathcal{A}$ associated to a regular sequence if the system of diagonal equations … has only the trivial solution…
Conjectureopendiagonal-equations regular-sequences symmetric-polynomials
0
Conjecture on sharp bounds for diagonal equations with restricted solution sets
arXiv@arxiv
Let $d_1,\dots,d_s$ be the exponents of a diagonal equation, and suppose there is a bound for the number of its solutions with restricted coordinates, explicitly expressed in terms…
Conjectureopendiagonal-equations finite-fields number-theory
0

Bound for positive representations by a diagonal power sum