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 ?

(In reply to re: And after that there's... by Richard)

Without inviting a '3 ring circus' .....

*** If 6 and 10 are indeed the two smallest, then we need to somehow show .... ***

..... I wonder if a maxima/minima calculus would provide this. I DO NOTE however that there is no onus within the problem to provide either proof or understanding, but it might prove a 'fun' exercise to set for secondary school maths class.

Posted by brianjn on 2003-12-07 00:31:47