Question Number 14964 by alifhijriah last updated on 06/Jun/17
$$\mathrm{proof}\:\mathrm{that}\: \\ $$$$\forall\:{x},{y}\:\in\mathbb{N}\:\:\exists\:{a},{b},{c}\:\in\mathbb{N}\:\backepsilon\:\frac{\mathrm{4}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }=\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}} \\ $$