2 problems

Let $v_2(n)$ denote the exponent of $2$ in a positive integer $n$, and let $a,b,c$ be positive integers. Non-almost-universality conjecture. (i) If $v_2(b)\ge v_2(c)$,…

For $k,l\in\mathbb{N}$, define the mixed quadratic-triangular form … where $T_z=z(z+1)/2$. Sun's conjecture. For every $k,l\in\mathbb{N}$, the form $2^kx^2+2^ly^2+T_z$ is almost un…