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Find-all-pairs-of-positive-integers-a-b-such-that-a-2-2ab-2-b-3-1-Z-




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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