Question

Arata ca numarul 5 la puterea 2018 poate fi scris ca o suma de doua patrate perfecte

Answer 1

Răspuns:

5^2018=

=5^2016*5^2=

=5^2016*25=

=5^2016*(16+9)=

=5^2016*(4^2+3^2)=

=5^2016*4^2+5^2016*3^2=

=(5^1008)^2*4^2+(5^1008)^2*3^2=

= (5^1008*4)^2+(5^1008*3)^2 - suma de patrate perfecte