Determine all possible pairs of positive whole numbers (v, w) satisfying the following equation:

v³ – w³ = vw + 61

Set a=b+x.

Then the equation can be expressed as

b(b+x)(3x-1) = 61 - x^3.

For the rhs to be positive x=1,2,3.

But only for x=1 is rhs divisible by (3x-1).

So b(b+1)=30 and a=6, b=5 as Josie found.

 

Posted by xdog on 2007-07-22 20:36:32