Question

determinați numerele naturale a si b stiind ca (a,b)=28 si [a,b]=784.

Answer 1

[tex]a\cdot b=(a,b)\cdot [a,b]\\ a\cdot b=28\cdot 784=28^3\\ (a,b)=28, \rightarrow a=28u,b=28v,(u,v)=1\\ a\cdot b=28^3=28^2\cdot uv\\ uv=28\\ u=1,v=28,\\ a=28,b=784\\ u=2,v=14 , nu convine\\ u=4,v=7\\ a=112,b= 196\\ u=7,v=4\\ a=196,b=112\\ u=14,v=2 nu convine\\ u=28,v=1\\ a=784,b=28 [/tex]