Question Number 184567 by a.lgnaoui last updated on 08/Jan/23
$${Resoudre}\:{dans}\:\mathbb{Z}^{+} \\ $$$$\sqrt{{a}}\:\:+\sqrt{{b}}\:={z}\:\:\:\:\left({a},{b},{z}\right)\in\mathbb{N}^{\mathrm{3}} \\ $$$${a},{b}\:? \\ $$
Answered by Frix last updated on 08/Jan/23
$${a}={n}_{\mathrm{1}} ^{\mathrm{2}} \wedge{b}={n}_{\mathrm{2}} ^{\mathrm{2}} \\ $$$$\Rightarrow \\ $$$${z}=\sqrt{{a}}+\sqrt{{b}}={n}_{\mathrm{1}} +{n}_{\mathrm{2}} \\ $$
Commented by a.lgnaoui last updated on 08/Jan/23
$${n}_{\mathrm{1}} ?\:\:\:\:\:{n}_{\mathrm{2}} ? \\ $$
Commented by Frix last updated on 08/Jan/23
$${n}_{\mathrm{1}} \in\mathbb{N};\:{n}_{\mathrm{2}} \in\mathbb{N} \\ $$