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Find all solutions.....

\(4x^{3}\) \(-\) \(3x\) \(-1\) \(=\) \(2y^{2}\). Find all positive integral solutions.... I solved it and I found that there will be infinitely many sol. \(x\) = \(2k^{2} + 1\),, \(y\) = \(4k^{3} + 3k\) where k is any positive integer....... Please verify whether I am correct.....

Note by Alpha Beta
3 years, 3 months ago

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Yes, provided that \(x, y\) are positive integers, you are correct. But, it also holds for negative \(k\) such that \(y\) is negative. Aditya Parson · 3 years, 3 months ago

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