Question

Aratati ca 2011 la puterea 2011 poate fi scris ca o suma de 5 patrate perfecte

Answer 1

2011^2011=(2011^2010) *2011=

(1600+400+9+1+1)*2011^2010=

(1600+400+9+1+1)*(2011^1005)²=

(40²+20²+3²+1²+1²)*(2011^1005)²=
{40*(2011^1005)]² +[20*(2011^1005)]²+[3*(2011^1005)]²+(2011^1005)²+(2011^1005)²
o suma de 5 patrate perfecte
nu ni s-a pus conditia ca toti termenii sumei sa fie diferiti intre ei