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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Solution, I think

| Comment 1 of 3

Simplify the equation to read xy = 2010x + 2010y

Then ( x - 2010 )( y - 2010 ) = 2010^2 = (2*3*5*7)^2

Since each of the 4 primes is a square, there are 3*3*3*3 = 81 different factors of the RHS and 81 different (x,y) solutions.

Posted by xdog on 2010-10-15 14:34:46

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