Răspuns:
a) 676
b) 2000
Explicație pas cu pas:
A(n)=20192019...20192019
A(1)=2019
A(2)=20192019
a)
(A(n) - 9):10 = 20192019...2019201
Dar (2+0+1+9)·x+2+0+1 = 2019:
⇒ 12·x+3 = 2019 ⇒ 12·x = 2016 ⇒
⇒ x = 2016/12 ⇒ x = 168
⇒ A(n) are 168·4+4 = 676 de cifre
b)
[tex]A(519) - A(500) = 20192019\underset{\text{de 519 ori}}{\underbrace{...}}2019 - 20192019\underset{\text{2019 de 500 ori}}{\underbrace{...}}2019[/tex]
[tex]A(519) - A(500) = 20192019\underset{\text{2019 de 519-500 ori}}{\underbrace{...}}0000\underset{\text{de }4\cdot\text{500 ori}}{\underbrace{...}}0000[/tex]
Înseamnă că B = A(519) - A(500) are 4·500 = 2000 de zerouri la final.
