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Problem. Is there a prime number $p$ (desirably $p\le 3$) and an infinite set $A\subset\mathbb N$ such that for any distinct numbers $a,b\in A$ the Diophantine equation $x^p+ax=y^p+by$ has no positive integer solutions?
Problem. Is there a prime number $p$ and an infinite set $A\subset\mathbb N$ such that for any distinct numbers $a,b\in A$ the Diophantine equation $x^p+ax=y^p+by$ has no integer solutions?
Problem. Is there a prime number $p$ (desirably $p\le 3$) and an infinite set $A\subset\mathbb N$ such that for any distinct numbers $a,b\in A$ the Diophantine equation $x^p+ax=y^p+by$ has no positive integer solutions?
Problem. Is there a prime number $p$ and an infinite set $A\subset\mathbb N$ such that for any distinct numbers $a,b\in A$ the Diophantine equation $x^p+ax=y^p+by$ has no integer solutions?
