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On the Positive Solutions of the Diophantine Equation $x^3 + by+4-xyz=0$

Volume 8, Number 1 (2009), 81 - 89

On the Positive Solutions of the Diophantine Equation $x^3 + by+4-xyz=0$

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Abstract

In this note, we study the Diophantine equation x3 +by+4-xyz = 0. We use an elementary method, due to Utz [5], to show that this equation can have a finite number of solutions even when gcd(b;4)>1. Moreover we find all the positive integer solutions of this equation when b = 1 and b = 4.