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Look for the pairs (Posted on 2010-10-15) Difficulty: 3 of 5
Find the number of positive integer pairs (x; y) satisfying:

Try to generalize for 1/n.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

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Solution No Subject | Comment 2 of 3 |
Well, xdog has done all the heavy lifting, except for a small typo.
2010 factors as 2*3*5*67.  Answer is still 81.

In general,
(x-n)(y-n) = n^2,
so the number of satisfying pairs is just the number of divisors of n^2.

Edited on October 15, 2010, 2:45 pm
  Posted by Steve Herman on 2010-10-15 14:41:30

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