x+y+z=26
{x,y,z}i.p{2,3,4} =K => x=K/2 , y=K/3 , z=K/4
K/2+K/3+K/4=26 (numitorul comun este 12) => 6K/12+4K/12+3K/12 =26 |•12
6K+4K+3K=26
13K=26
K=26/13
K=2 =>
x=2/2=1
y=2/3
z=2/4
Verificare: 1+2/3+2/4=26 (numitorul comun este 12)
12/12+8/12+6/12|•12
12+8+6=26