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proof-that-x-y-N-a-b-c-N-4-x-2-y-2-1-a-1-b-1-c-




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

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