Determine the minimum value of a positive integer constant c such that the equation xy³ - y³+ x + y = c has precisely four distinct solutions in positive integers.

I used the reduce function in Mathematica to find the number of positive solutions for each c starting at c=1 and kept looking until I found the first one with 4 solutions.  And that was c=200 with solutions (x,y): (1,199) (4,4) (8,3) and (100,1)

 

Now I did notice that (1,c-1) is a solution for all c>1 as well as (c/2,1) for all even c>1.

Posted by Daniel on 2009-05-02 20:14:02