Question

Impartind numarul natural n la numerele 18,30 si 24, se obtin caturi nenule si de fiecare data restul 2
a) Aflati cel mai mic numar n cu aceasta propietate
b) Aflati toate numere n cu aceasta propietate astfel incat 1500 <n< 2500​

Answer 1

Răspuns:

a) n:18=c₁ rest 2=>n=18c₁+2=>n-2=18c₁

n:30=c₂ rest 2=>n-2=30c₂

n:24=c₃ rest 2=>n-2=24c₃

18 = 2·3²

30 = 2 ·3 ·5

24 = 2³·3

n-2=cmmmc(18,24,30)=2³·3²·5=8·9·5=360

n-2=360=>n=360+2=>n=362

362:18=20 rest2

362:30=12 rest 2

362:24=15 rest 2

b) 1500 <n< 2500​

M₃₆₂=362, 724, 1086, 1448, 1810, 2172, 2534

1500 < 1810+2;2172+2 < 2500

n=1812,2174