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More Harmonic Integers (2) (Posted on 2007-03-28) Difficulty: 3 of 5
Consider three positive integers x< y< z in Harmonic Sequence.

Determine all possible values of the positive integer constant S for which the equation 15x + Sy = 15z admits of valid solutions.

See The Solution Submitted by K Sengupta    
Rating: 2.5000 (2 votes)

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Hints/Tips Hint | Comment 2 of 6 |
(In reply to a few found by brute force.... by Dej Mar)

1. Looking at the evaluated values it seems that  8^2 + 15^2 = 17^2; 20^2 + 15^2= 25^2, and so on.

So, S^2 + 15^2 appears to be a perfect square for these values of S. (Why?)

2. Since S must be a positive integer, the value S=0 is not valid.

  Posted by K Sengupta on 2007-03-29 09:35:39
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