What are the two smallest positive whole numbers the difference of whose squares is a cube and the difference of whose cubes is a square ?

I plugged a bunch of numbers into an Excel spreadsheet.  I ended up taking the cubed root of (a1^2)-36 and the square root of (a1^3)-216 and figuring out where they both yielded integers.  Why 36 and 216?  By trial and error, I used (a,a^2,a^3) --> (1,1,1), (2,4,8), (3,9,27),...until (6,26,216) worked.  The two numbers that yielded the correct solution were 10 and 6.  Snoogins.

Posted by Marc on 2005-06-07 18:37:41