Question

Sa se determine toate numerele naturale mai mari ca 250 si mai mici ca 1200 care impartite la 28,35,40 si 70 dau de fiecare data restul 7.

Answer 1

x:28=c rest7  ⇒x=28c+7     ⇒x-7=28c
x:35=c rest 7  ⇒x=35c+7   ⇒x-7=35c
x:40=c rest 7  ⇒x=40c+7   ⇒x-7=40c
x:70=c rest 7   ⇒x=70c+7  ⇒x-7=70c

x-7∈M[28,35,40,70]
28=7·2²
35=7·5
40=2³·5
70=7·2·5
[28,35,40,70]=2³·7·5=280
M280={280,560,840,1120,1400....]
X-7=280
X=280+7
X=287
287:28=10 REST 7
287:35=8 rest 7
287:40=7 rest 7
287:70=4 rest 7
deci nr.cuprinse intre 250 si 1200 sunt:280+7, 560+7,840+7,1120+7
in concluzile nr.care satisfac conditiile mentionate mai sus sunt:
287,567,847,si 1127