A Note on the Exponential Diophantine Equation 8^x + 161^y = z²

Abstract

In this note, we revisit the exponential Diophantine equation 8x + 161y = z2, initially studied by Manikandan and Venkatraman. Their work established that the equation has the two non-negative integer solutions: (1, 0, 3) and (1, 1, 13). Our findings reveal an additional solution, (2, 1, 15), and we show that these three solutions constitute the complete list of non-negative integer solutions for this equation. This extends and completes the main result presented in their paper.