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Another 2006 Problem (Posted on 2006-09-30) Difficulty: 2 of 5
Determine the total number of positive integer solutions of:

2/x + 3/y = 1/2006

See The Solution Submitted by K Sengupta    
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re(2): Solution | Comment 4 of 8 |
(In reply to re: Solution by xdog)

I think it should be pointed out that half the square root of 2^3 * 3 * 17^2 * 59^2 is over 2006, and therefore, in order for the left side of your factored equation to have two negative factors, at least one of x and y would have to be negative.  Otherwise it would be conceivable to have positive x and y accounting for two negative factors of the same absolute value as other solutions, as you have to add 4012 to one factor and 6018 to the other to get x and y, bringing the total number over 72.

Actually, come to think about it, since 6018 (=3*2006) is added to one of the factors to get y, half the square root is too lenient a test, that having been based on 2*2006.

Edited on September 30, 2006, 2:07 pm
  Posted by Charlie on 2006-09-30 13:49:50

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