Question

Aflati toate umerele naturale mai mici decat 2000 care impartite la 24 30 si 18 dau de fiecare data restul 7.
Dau coroita,

Answer 1

x = nr căutat
x<2000

x:24=c1 rest 7
x:30=c2 rest 7
x:18=c3 rest 7
x=?
D=C•Î+R

x=24c1+7 => x-7=24c1 => (x-7) divizibil cu 24
x=30c2+7 => x-7=30c2 => (x-7) divizibil cu 30
x=18c3+7 => x-7=18c3 => (x-7) divizibil cu 18
=> x=c.m.m.m.c. al nr. 24;30;18

24=2³•3
30=2•3•5
18=2•3²
—————
[24;30;18]=2³•3²•5=8•9•5=9•40=360

x-7=360
x=360+7
x=367 (A)

x-7=2•360
x-7=720
x=720+7
x=727 (A)

x-7=3•360
x-7=1080
x=1080+7
x=1087 (A)

x-7=4•360
x-7=1440
x=1440+7
x=1447 (A)

x-7=5•360
x-7=1800
x=1800+7
x=1807 (A)

Deci nr sunt : 367 ; 727 ; 1087 ; 1447 ; 1807