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Rezolvarea exercitiului :Aratati ca 100 la puterea 2013 se poate scrie ca suma de doua patrate perfecte.

Răspuns :

100^2013=100*100^2012 *=(64+36)100^2012= 64*100^2012+36^100^2012=

8² * (100^1006)²+ 6² * (100^1006)²= (8*100^1006)² +(6* 100^1006)²=a²+b², suma de 2 patrate perfecte, cerinta