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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
4 years, 5 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.

- 4 years, 5 months ago