On the Diophantine equation x ² − kxy + y ² + lx = 0

Abstract

Let l be a given nonzero integer. The authors give an explicit characterization of the positive integer k that makes the Diophantine equation x ² − kxy + y ² +lx = 0 have infinitely many positive integer solutions (x, y).

Keywords

Quadratic Diophantine equation / Solvability / Counting solutions

References

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