Abstract:In this paper we have shown that the Diophantine equation 8 x + 113 y = z 2 has exactly three non-negative integer solutions for x, y and z. The solutions are (1, 0, 3), (1, 1, 11) and (3, 1, 25) respectively.
Let n be an positive integer with n = 10(mod15). In this paper, we prove that (1,0,3) is unique non negative integer solution (x,y,z) of the Diophantine equation 8^x+n^y=z^2 where x y, and z are non-negativeintegers.
Let n be an positive integer with n = 10(mod15). In this paper, we prove that (1,0,3) is unique non negative integer solution (x,y,z) of the Diophantine equation 8^x+n^y=z^2 where x y, and z are non-negativeintegers.
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