Question

Aratati ca numatul 25la puterea n se poate scrie ca suma a doua patrate perfecte oarecare ar fi n numar natural nenul.

Answer 1

25^n=25*25^(n-1)=(9+16)*5^2(n-1)=(3^2+4^2)*5^2(n-1)=3^2*5^2(n-1) +4^2*5^2(n-1)=(3*5^(n-1))^2 + (4*5^(n-1))^2

Good night!