x,y,z>3 olur.
x≤y≤z olsun. Bu takdirde 1z≤1y≤1x ve 13=1x+1y+1z≤3x, x≤9 yani 4≤x≤9 elde edilir.
x=4 ise 13=14+1y+1z, 112=1y+1z≤2y, y≤24
1z=y−1212y, z=12yy−12=12+144y−12
13≤y≤24
(x=4,y=13,z=156),(x=4,y=14,z=84),(x=4,y=15,z=60),(x=4,y=16,z=48)(x=4,y=18,z=36),(x=4,y=20,z=30),(x=4,y=21,z=28),(x=4,y=24,z=24)
x=5 ise 13=15+1y+1z, 215=1y+1z≤2y, y≤15
1z=2y−1515y, z=15y2y−15=7+y2y−15
8≤y≤15.
(x=5,y=8,z=120),(x=5,y=9,z=45),(x=5,y=10,z=30),(x=5,y=12,z=20),(x=5,y=15,z=15)
x=6 ise 13=16+1y+1z, 16=1y+1z≤2y
y≤12
1z=y−66y, z=6yy−6=6+36y−6
7≤y≤12.
(x=6,y=7,z=42),(x=6,y=8,z=24),(x=6,y=9,z=18),(x=6,y=10,z=15),(x=6,y=12,z=12)
x=7 ise 13=17+1y+1z, 421=1y+1z≤2y
y≤10
1z=4y−2121y, z=21y4y−21=5+y+1054y−21
7≤y≤10.
(x=7,y=7,z=21)
x=8 ise 13=18+1y+1z, 524=1y+1z≤2y
y≤9
1z=5y−2424y, z=24y5y−24=4+4y+965y−24
8≤y≤9.
(x=8,y=8,z=12)
x=9 ise 13=19+1y+1z, 29=1y+1z≤2y
y=9
(x=9,y=9,z=9)
21 tane çözüm vardır.