Determine the total number of triplets (x, y, z) of positive integers, with x ≤ y ≤ z,
that satisfy this equation:

1/x + 1/y + 1/z = 7/15

Just for starters:

3,8,12 3,9,45 3,10,30 3,12,20 3,15,15

4,5,60 4,6,20 5,5,15 5,6,10 ...

7/15 is the repeating decimal 0.466666666--- so the other three integers just need to keep that pattern

edit for typo: first is 3,8,120 (not 3,8,12)

Repeating decimals might be 3 or 6 (or, of course, zero). I didn't find any more for z up to 500.( I see the previous entry had the same list as mine, but without the two with 15 as y and/or z. I don't think the problem as worded excludes those values. Probably none higher, since the repeating decimals would start later, but I haven't proven this.

*Edited on ***July 2, 2010, 2:12 pm**