On Sidon sets with squares, cubes and quartics in short intervals

M. Z. Garaev, F. M. Garayev, S. V. Konyagin

Representative examples of our results are as follows. For any positive integer $N$ the equation $$x^3+y^3=z^3+t^3,x,y,z,t\in \mathbb{N},\{x,y\}\ne \{z,t\}$$ has n…