Question

Aratati ca 2020^2021 poate fi scris ca o suma de 7 patrate perfecte

Answer 1

2020^2021 = 2020 * 2020^2020

Daca aratam ca 2020 poate fi scris ca suma de 7 patrate perfecte exercitiul este gata.

2020 = 1936 + 64 + 16 + 1 + 1 + 1 + 1 = 44^2 + 8^2 + 4^2 + 1^2 + 1^2 + 1^2 + 1^2

Deci 2020 * 2020^2020 = (44^2 + 8^2 + 4^2 + 1^2 + 1^2 + 1^2 + 1^2)*2020^2020 = (44*2020^1010)^2 + (8*2020^1010)^2 + (4*2020^1010)^2

+ (1*2020^1010)^2 + (1*2020^1010)^2+ (1*2020^1010)^2+ (1*2020^1010)^2;