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Divide The Cubic, Get The Pairs (Posted on 2007-05-26) Difficulty: 3 of 5
Find all possible positive integers (p,q) with p≤q such that (q³+1)/(pq-1) is an integer.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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re: Solution (a few questions) | Comment 4 of 5 |
(In reply to Solution by Brian Smith)

I don't follow some of the statements quoted below:

If q=2 then q^3+1 is odd and then both factors must be odd.

To which two factors does this refer?

Also,

If (p*n)^2 - 4*(p+n) = (p*n-2)^2 then 0 = 4, which is false.

Multiplying out both sides, I get:

(p*n)^2 - 4*(p+n) = (p*n)^2 - 4*(p*n) + 4, which becomes:

4*(p*n) - 4*(p+n) = 4.  How is the left side of this equation 0?

  Posted by ken on 2007-05-27 20:12:01
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