Ecuatie diofantiana cu o suma de inverse

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Filip Chindea
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Ecuatie diofantiana cu o suma de inverse

Post by Filip Chindea »

Fie \( n \in \mathbb{N} \) impar, \( n > 3 \), nedivizibil cu \( 3 \). Aratati ca exista \( a, b, c \in \mathbb{N} \) distincte si impare, astfel ca

\( \frac{3}{n} = \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \).

Concursul "La Scoala cu Ceas", 2008, Problema 6
Life is complex: it has real and imaginary components.
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