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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.

 Jul 17, 2021
 #1
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There are this many ways:

       a     b    c

1  = 180 60 9
2  = 126 70 9
3  = 120 72 9
4  = 90 90 9
5  = 180 36 10
6  = 130 39 10
7  = 120 40 10
8  = 105 42 10
9  = 90 45 10
10  = 80 48 10
11  = 75 50 10
12  = 66 55 10
13  = 60 60 10
14  = 110 30 11
15  = 120 24 12
16  = 100 25 12
17  = 70 28 12
18  = 60 30 12
19  = 45 36 12
20  = 40 40 12
21  = 156 20 13
22  = 84 20 14
23  = 70 21 14
24  = 35 30 14
25  = 90 18 15
26  = 60 20 15
27  = 40 24 15
28  = 30 30 15
29  = 120 16 16
30  = 48 20 16
31  = 45 18 18
32  = 36 20 18
33  = 30 20 20
34  = 28 21 20
35  = 24 24 20

 Jul 18, 2021

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