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In this paper we prove that the Diophantine equation 3 + 13 = z has exactly four non-negative integer solutions for x, y and z. The solutions are (1, 0, 2), (1, 1, 4), (3, 2, 14) and (5, 1, 16) respectively. AMS Subject Classification: 11D61

ON THE DIOPHANTINE EQUATION $ 3^x + 13^y = z^2 $