Question

Determinati numerele naturale a si b,pentru care avem:
(a,b)=15 si a + b=225

Answer 1

Explicație pas cu pas:

(a,b)=15 => a=15m si b=15n unde (m,n)=1

a+b=225 =>15m+15n=225 => 15(m+n)=225=>m+n=15

=>

m=1 n=14=>a=15 b=210

m=14 n=1=>a=210 b=15

m=7 n=8 => a=105 b=120

m=8 n=7=>a=120 b=105

(a,b)€{(15,210),(210,15),(105,120),(120,105)}