Question Number 166400 by naka3546 last updated on 20/Feb/22
$$\mathrm{Find}\:\:\mathrm{all}\:\:\mathrm{pairs}\:\:\mathrm{of}\:\:\mathrm{positive}\:\:\mathrm{integers}\:\left({a},{b}\right)\:\:\mathrm{such}\:\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\frac{{a}^{\mathrm{2}} }{\mathrm{2}{ab}^{\mathrm{2}} \:−\:{b}^{\mathrm{3}} +\mathrm{1}}\:\:\in\:\:\mathbb{Z}^{+} \\ $$