Question

Daca a,b,c apartin lui N si 11a+33b=c => 11 | 5c+22

Answer 1

11a+33b=c
11(a+3b)=c

5c+22=5×11(a+3b)+22=
=11×5(a+3b)+11×2=
=11×[5(a+3b)+2] ⋮ 11 => 11 | (5c+22)

Answer 2

11a+33b=c

11(a+3b)=c   notam a+3b =m
deci c=11·m
5c+22 =5·11·m+22= 5·11·m+2·11=11(5m+22)
 deci   11|5c+22