M. Z. Garaev

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

Abstract Representative examples of our results are as follows. For any positive integer $$N$$ N the equation $$x^3+y^3=z^3+t^3, \quad x,y,z,t\in \mathbb{N}, \quad \{x,y\}\not=\{z,t\}$$ x 3 + y 3 = z 3 + t 3 , x , y , z , t ∈ N , { x , y } ≠ { z , t } has no solutions satisfying...