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Expression Ratio (Posted on 2013-09-03) Difficulty: 4 of 5
Determine all pairs (a,b) of positive integers with a > b, for which (a2+b2)/(a-b) is an integer which divides 1995.

Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
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Method | Comment 3 of 4 |
Let n be a factor of 1995
(a2+b2)/(a-b) = n
(a2+b2) = n*(a-b)
a2-na+ b2+nb = 0
which is quadratic in a so

For each value of n there are only a few values of b that yield real solution so from there I went brute force and got the same list as Charlie.

Note: Only multiples of 5 seem to have solutions.  I plan to look a little deeper.

  Posted by Jer on 2013-09-04 13:28:20
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