Conc.interj."Pitagora"Rm.Valcea 2010 Subiectul II

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Andi Brojbeanu
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Conc.interj."Pitagora"Rm.Valcea 2010 Subiectul II

Post by Andi Brojbeanu »

a) Sa se arate ca ecuatia \( \sqrt{x+y\sqrt{2010}}+\sqrt{x-y\sqrt{2010}}=\sqrt{4020} \) are un numar finit de solutii \( (x,y)\in \mathb{N}*X\mathb{N}* \).
b) Demonstrati ca numarul \( 2010^{2010}+1 \) nu poate fi scris ca suma a doua numere prime.
Prof. Ion Predescu, Pesceana
Prof. Constantin Barascu, Rm. Valcea
Brojbeanu Andi Gabriel, clasa IX-a
Colegiul National "Constantin Carabella" Targoviste
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