[tex]a = {2}^{0} + {2}^{1} + ... + {2}^{2019} [/tex]
[tex]2a = {2}^{1} + {2}^{2} + ... + {2}^{2020} [/tex]
---------------------------------------------------(--)
[tex]a = {2}^{2020} - {2}^{0} [/tex]
[tex]a = {2}^{2020} - 1 [/tex]
[tex]u(a) = u( {2}^{2020} ) - u(1)[/tex]
[tex]u( {2}^{2020} ) = ?[/tex]
2¹=2. 4k=u(...6).
2²= 4. 4k+1= (...2)
2³=8. 4k+2= (...4)
2⁴=16. 4k+3= (...8)
2020:4= 502 rest 0=> 4k= (...6)
[tex] = > u( {2}^{2020} ) = 6[/tex]
[tex]u(a) = 6 - 1 = 5 [/tex]
u(a)=5 => numarul a se divide cu 5
