In how many different ways can 2/15 be represented as 1/a + 1/b + 1/c, if a and b and c are positive integers with a >= b >= c.
+23245 At the website http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptian.html
they found 72 ways to express 2/15 into Egyptian fractions with 3 fractions.
Well, I found at least 80 "modern fractions" ! I only checked numbers up to 10,000.
1 = (1560, 130, 8)
2 = (1320, 132, 8)
3 = (1080, 135, 8)
4 = (1020, 136, 8)
5 = (920, 138, 8)
6 = (840, 140, 8)
7 = (720, 144, 8)
8 = (696, 145, 8)
9 = (600, 150, 8)
10 = (570, 152, 8)
11 = (520, 156, 8)
12 = (480, 160, 8)
13 = (440, 165, 8)
14 = (420, 168, 8)
15 = (408, 170, 8)
16 = (360, 180, 8)
17 = (345, 184, 8)
18 = (320, 192, 8)
19 = (312, 195, 8)
20 = (300, 200, 8)
21 = (280, 210, 8)
22 = (270, 216, 8)
23 = (264, 220, 8)
24 = (240, 240, 8)
25 = (720, 48, 9)
26 = (450, 50, 9)
27 = (270, 54, 9)
28 = (180, 60, 9)
29 = (126, 70, 9)
30 = (120, 72, 9)
31 = (90, 90, 9)
32 = (930, 31, 10)
33 = (480, 32, 10)
34 = (330, 33, 10)
35 = (255, 34, 10)
36 = (210, 35, 10)
37 = (180, 36, 10)
38 = (130, 39, 10)
39 = (120, 40, 10)
40 = (105, 42, 10)
41 = (90, 45, 10)
42 = (80, 48, 10)
43 = (75, 50, 10)
44 = (66, 55, 10)
45 = (60, 60, 10)
46 = (1320, 24, 11)
47 = (110, 30, 11)
48 = (420, 21, 12)
49 = (220, 22, 12)
50 = (120, 24, 12)
51 = (100, 25, 12)
52 = (70, 28, 12)
53 = (60, 30, 12)
54 = (45, 36, 12)
55 = (40, 40, 12)
56 = (1170, 18, 13)
57 = (156, 20, 13)
58 = (84, 20, 14)
59 = (70, 21, 14)
60 = (35, 30, 14)
61 = (240, 16, 15)
62 = (90, 18, 15)
63 = (60, 20, 15)
64 = (40, 24, 15)
65 = (30, 30, 15)
66 = (120, 16, 16)
67 = (48, 20, 16)
68 = (45, 18, 18)
69 = (36, 20, 18)
70 = (30, 20, 20)
71 = (28, 21, 20)
72 = (24, 24, 20)
73 = (1920, 128, 8)
74 = (1720, 129, 8)
75 = (2520, 126, 8)
76 = (2070, 46, 9)
77 = (3720, 124, 8)
78 = (3000, 125, 8)
79 = (4920, 123, 8)
80 = (7320, 122, 8)
