Question

Aratati ca numarul 29 la puterea 501 se poate scrie ca o suma de doua patrate perfecte

Answer 1

$29^{501} =29*29^{500} =(25+4)*29^{500} = \\ (5^{2} +2^{2} )*29^{500}=5^{2}*29^{500}+2^{2}*29^{500}= [5*29^{250}]^{2} +[2*29^{250}]^{2}$