Find all possible positive integers (p,q) with p≤q such that (q³+1)/(pq-1) is an integer.

(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