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Reciprocal Equation #3 (Posted on 2010-07-02) Difficulty: 3 of 5
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

No Solution Yet Submitted by K Sengupta    
Rating: 2.0000 (1 votes)

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some starters | Comment 2 of 5 |

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
  Posted by ed bottemiller on 2010-07-02 13:47:56

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