perplexus.info :: Just Math : Look for the pairs

Look for the pairs (Posted on 2010-10-15)

Find the number of positive integer pairs (x; y) satisfying:
1/x+1/y=1/2010

Try to generalize for 1/n.

No Solution Yet Submitted by Ady TZIDON

Rating: 4.0000 (1 votes)

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| 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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