3 problems

Kollár–Villarino conjecture. The following conditions are equivalent:

Euler's conjecture concerns representations of a $k$th power as a sum of powers. Euler's conjecture. In $1753$, Leonhard Euler conjectured that it would take at least $k$ $k$th pow…

Let $u$ be a positive integer, let $P_{2,4u}$ denote the cone of positive semidefinite binary forms of degree $4u$, and let $W_{2,(u,4)}$ denote the cone of sums of $u$ fourth powe…