Question

Aflati toate nr de trei cifre care impartite la 15 35 si 63 dau de fiecare data restul 11

Answer 1

d=c*i+r, r<i
d=$c_{1}$*15+11⇒d-11=$c_{1}$*15
d=$c_{2}$*35+11⇒d-11=$c_{2}$*35
d=$c_{3}$*63+11⇒d-11=$c_{3}$*63
din cele 3 relatii⇒  "d-11"  M comun al nr 15, 35, 63
[15, 35, 63]=315 ⇒ luam M 315 de 3 cifre= {315, 630 , 945 }
d-11=315⇒d=326 ; d-11=630⇒d=641;  d-11=945⇒d=956
Deci d ∈{326, 641, 956}

Answer 2

d=c*i+r, r<i
d=*15+11⇒d-11=*15
d=*35+11⇒d-11=*35
d=*63+11⇒d-11=*63
din cele 3 relatii⇒  "d-11"  M comun al nr 15, 35, 63
[15, 35, 63]=315 ⇒ luam M 315 de 3 cifre= {315, 630 , 945 }
d-11=315⇒d=326 ; d-11=630⇒d=641;  d-11=945⇒d=956
Deci d ∈{326, 641, 956}