Question

Numerele 2126, 1634 si 1984 impartite la acelasi numar natural dau resturile 26, 14, 4. Aflati impartitorul.

Answer 1

2126=na+26
1634=nb+14
1984=nc+4


2100=na
1620=nb
1980=nc

n|(2100,1620,1980)
si
n>26

n|(210,162,198)*10
n|(35,27,33)*60
 35=5*7
27=3³
33=3*11
deci (35,27,33)=1 si atunci  (210;162,198)=60

deci n|60 si n>26
n poate fi 30 sau 60

care verifica fiecare  dintre ele  toate cerintele
Verificare 
2126:30=70 rest 26
2126:60=35 rest 26

1634:30=54 rest 14
1634:60=27 rest 14

1984:30=66 rest4
1984:60=33 rest4

Answer 2

2126:a=c rest 26=>2126=a*c+26=>2126-26=a*c=>2100=a*c
1634:a=c rest 14=>1634=a*c+14=>1634-14=a*c=>1620=a*c
1984:a=c rest 4=>1984=a*c+4=>1984-4=a*c=>1980=a*c
2100=210
1620=162
1980=198
cmmdc= 60.
n=(35,27,33)=1
n>26=>n=30 sau 60