Roth-type Theorem for high-power system in Piatetski-Shapiro primes (II)

Xiumin Ren, Yu-chen Sun, Qingqing Zhang +1

We consider the nonlinear system $c_1{p}_1^d+c_2{p}_2^d+\cdots +c_s{p}_s^d=0$ with $c_1,c_2,\dots ,c_s\in \mathbb{Z}$ being nonzero and satisfying $c_1+c_2+\cdots +c_s=0$. We s…