Question

Determinati numerele naturale nenule a si b, cu a (a,b)=15 {a,b}=360

Answer 1

cum (a,b)=15 => 
a=15*k            ,k , p prime intre ele ;  k,p  nr naturale, nenule
b=15*p

cum [a,b] =360 => 3*5*k*p=360=>k*p=24 iar cum (k,p) =1 => 
=> k=1,p=24
     k=3,p=8
     k=8,p=3
     k=24,p=1
cum a=15*k  si b=15*p =>
=> (a,b) ={ (15,360),(45,120),(120,45),(360,15)}