Question Number 185386 by Rupesh123 last updated on 20/Jan/23
Commented by floor(10²Eta[1]) last updated on 21/Jan/23
$$\mathrm{a}^{\mathrm{2}} +\mathrm{2ab}+\mathrm{b}^{\mathrm{2}} +\mathrm{1990a}+\mathrm{1990b}+\mathrm{36}= \\ $$$$=\mathrm{a}^{\mathrm{2}} +\mathrm{1990a}+\mathrm{36}+\mathrm{b}^{\mathrm{2}} +\mathrm{1990b}+\mathrm{36} \\ $$$$\Rightarrow\mathrm{2ab}=\mathrm{36}\Rightarrow\mathrm{ab}=\mathrm{18} \\ $$$$\left(\mathrm{a},\mathrm{b}\right)=\left\{\left(\mathrm{18},\mathrm{1}\right),\left(\mathrm{9},\mathrm{2}\right),\left(\mathrm{6},\mathrm{3}\right),\left(\mathrm{3},\mathrm{6}\right),\left(\mathrm{2},\mathrm{9}\right),\left(\mathrm{1},\mathrm{18}\right)\right\} \\ $$