Question

Determinati numerele naturale mai mare ca 900 si mai mici decat 1600 care impartite la 12,28 si,respectiv,36 dau de fiecare data restu 7

Answer 1

 n=12xc1+7=28xc2+7=36xc3+7

n-7=12xc1=28xc2=36xc3

n-7=M [12,28,36]

n-7=M 252

n-7={252,2x252,3x252,4x252,5x252….}   n-7={252,504,756,1008…}

dar  900<n<1600

     900-7<n-7<1600-7

          893<n-7<1593

=>893<4x252   si   6x252<1593

    893<1008 si 1512<1593

n-7={4x252,5x252,6x252}  n-7={1008, 1260, 1512}

=>n={1015,1267,1519}