On two conjectures for generalized off-diagonal Schur numbers

Yanyan Song, Yaping Mao

For an integer $t\ge 3$, let $\mathcal{L}(t)$ denote the linear equation $x_1+x_2+\cdots +x_{t-1}=x_t,$ where all variables are positive integers. For integers $k\ge 1$…