Question

1) Sa se gaseasca cel mai mic numar natural care imaprtit cu 5 si 7 da accelasi rest 1.
2) Aflati toate numerle mai mici decat 1000 care impartite cu 24:18:20 dau accelasi rest 9.
3) Aflati 2 numere naturale care au produsul 96 si c.m.m.d.c 2.
Fast pls

Answer 1

1) n:5=c rest 1
    n:7=c rest 1....=> n=5*7+1...=> n=35+1....=>n=36
  
36:5=7 rest 1
36:7=5 rest 1

2) n:24=c rest 9
    n:18=c rest 9
    n:20=c rest 9.....=>n=18*20+9...=> n=360+9...=>n=369

369:24=15 rest 9
369:18=20 rest 9
369:20=18 rest 9

n=369*2-9...=> n=738-9....=> n=729

729:24=30 rest 9
729:18=40 rest 9
729:20=36 rest 9

n=(369 si 729) ...urmatorul nr. care indeplineste conditia este 1089>1000

3) cmmdc(x;y)=2...unde x*y=92...=> x=92:2...=>x=48...=>y=2
    cmmdc(48;2)=2