Mathematical analysis demonstrates no non-negative integer solutions for two exponential Diophantine equations, highlighting constraints on prime power sums yielding squares.
In this paper, we consider the non-linear Diophantine equations 61 x + 67 y = z 2 and 67 x + 73 y = z 2 , where x, y and z are non-negative integers. It has been shown that these non-linear Diophantine equations have no solution.
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Kumar et al. (2018) studied this question.
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