Question

Determinati numerele naturale a, b, daca (a, b)= 8 si a*b= 768. Dau coronita!

Answer 1

sc[tex]\text{Avem:}\\ a=8d_1 \\ b=8d_2 \\ (d_1,d_2)=1 \\ab=64d_1d_2=768 \Rightarrow d_1d_2=12\\ \text{Cautam perechi de numere prime intre ele, al caror produs e 12 }: \\ d_1=1,d_2=12 \Rightarrow a=8,b=96 d_1=3,d_2=4\Rightarrow a=24,b=32 \\ \text{Se adauga si solutiile reciproce.}[/tex]