Question

comparati numarul divizorilor lui 2020 la puterea 2019 cu numarul divizorilor 2019 la puterea 2020​

Answer 1

Răspuns:

Descompunem pe 2020 si 2019 in factori primi

$2020=2^2\times 5\times 101 \\ \\ 2020^{2019}=2^{4038}\times 5^{2019}\times 101^{2019}$

Are (4038+1)(2019+1)(2019+1) = 4039×2020$^2$ divizori

2019 = 3 × 673

$2019^{2020}=3^{2020}\times 673^{2020}$

Are (2020+1)(2020+1) = 2020$^2$+2020+2020+1 = 2020$^2$+4041 divizori

Evident, primul are mai multi divizori