ON THE SOLUTION OF A CLASS OF EXPONENTIAL DIOPHANTINE EQUATIONS

Abstract

In this note, we show that for n = 4N + 3, N     N      0  , the expo- nential Diophantine equation n^x + 24^y = z² has exactly two solutions if n + 1 or equivalently N + 1 is an square. When N + 1 = m², the solutions are given by (0, 1, 5) and (1, 0, 2m). Otherwise it has a unique solution (0, 1, 5) in non-negative integers. Finally, we leave an open problem to explore.