Question

aflati numerele naturale x si y stiind ca [x,y] +(x,y)=119

Answer 1

(x,y)*[x,y]+(x,y)^2=119*(x,y)
x*y+(x,y)^2=119*(x,y)
x=md
y=nd, (m,n)=1, d=c.m.m.d.c al lui x si y
md*nd+d^2=119d
d(mn+1)=119=7*17

d=7, mn=16
m=1, n=16, x=7, y=112
m=2, n=8, x=14, y=56 nu
m=4, n=4, x=28, y=28 nu
m=8, n=2, x=56, y=14 nu
m=16, n=1, x=112, y=7

d=17, mn=6
m=1, n=6, x=17, y=102
m=2, n=3, x=34, y=51
m=3, n=2, x=51, y=34
m=6, n=1, x=102, y=17

x     7           17       34     51     102   112
y    112        102      51     34     17     7