On the exponential Diophantine equation mx+(m+1)y=(1+m+m2)z

Abstract

Let m > 1 be a positive integer. We show that the exponential Diophantine equation mx + (m + 1)y = (1 + m + m2)z has only the positive integer solution (x, y, z) = (2, 1, 1) when m ≥ 2.

Keywords

• exponential diophantine equations
• classification method
• primitive divisor theorem
• 11d61
• 11d75