Question

Aratati ca 29 la puterea2001 se poate scrie ca o suma de trei patrate perfecte.

Answer 1

29^2001 =>
= 29^(2000 + 1 ) =
= 29 x 29^2000 = 
= ( 4 + 9 + 16 ) x 29^2000 =
= ( 2^2 + 3^2 + 4^2 ) x 29^2000 =
= 2^2 x 29^2000 + 3^2 x 29^2000 + 4^2 x 29^2000 =
= ( 2 x 29^1000 )^2  +  ( 3 x 29^1000 )^2 + ( 4 x 29^1000 )^229^2001 =
 29 x29^2000 =( 4+9+16)x(29^1000)² = 2² x(29^1000)² + 3² x(29^1000)² + 
5² x(28^1000)² = (2 x29^1000)² +( 3 x29^1000)² + (5 x29^1000)²