Question

exercitiile 8, 9 si 10! urgent!!!

Answer 1

Salut,

8. a41b divizibil cu 10 → a = {1,2,3,4,5,6,7,8,9}
b = {0}.

1410, 2410, 3410, 4410, 5410, 6410, 7410, 8410, 9410.


9. a = 2+4+6+...+78
a = 2(1+2+3+...+39)

1+2+3+...+39 → suma lui Gauss : [n(n+1)]/2.

[39(39+1)]/2 = (39×40)/2 = 39×20 = 780.

a = 2×780
a = 1560 → a este divizibil cu 5.


10. abb divizibil cu 2 → a = {1;3;5;7;9}
b = {0;2;4;6;8}

100, 122, 144, 166, 188, 300, 322, 344, 366, 388, 500, 522, 544, 566, 588, 700, 722, 744, 766, 788, 900, 922, 944, 966, 988.


a = 1+2+3+...+100+51•101

1+2+3+...+100 → suma lui Gauss

[100(100+1)]/2 = (100•101)/2 = 50•101 = 5050.

a = 5050+51•101
a = 5050+5151
a = 10201 → 10201 = 101² → a este p.p.


Succes! :3