Aflarea numarului n

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Kramer
Arhimede
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Joined: Fri Nov 21, 2008 1:51 pm

Aflarea numarului n

Post by Kramer »

Determinati numerele naturale nenule n pentru care exista \( x,y \in\mathbb{R}_+ \) astfel incat:

\( \sqrt{x} + \sqrt{y} = 2 \)

\( \sqrt{x+n} + \sqrt{y+n}\in\mathbb{N} \)
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Marius Mainea
Gauss
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Joined: Mon May 26, 2008 2:12 pm
Location: Gaesti (Dambovita)

Post by Marius Mainea »

Se demonstreaza ca \( n=p^2-1,p\in\mathbb{N},p\ge 2 \) sau \( n=p^2+p-1,p\in\mathbb{N},p\ge 1 \).
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