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Question Number 166400 by naka3546 last updated on 20/Feb/22

Find  all  pairs  of  positive  integers (a,b)  such  that        (a^2 /(2ab^2  − b^3 +1))  ∈  Z^+

$$\mathrm{Find}\:\:\mathrm{all}\:\:\mathrm{pairs}\:\:\mathrm{of}\:\:\mathrm{positive}\:\:\mathrm{integers}\:\left({a},{b}\right)\:\:\mathrm{such}\:\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\frac{{a}^{\mathrm{2}} }{\mathrm{2}{ab}^{\mathrm{2}} \:−\:{b}^{\mathrm{3}} +\mathrm{1}}\:\:\in\:\:\mathbb{Z}^{+} \\ $$

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