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 ?

Set x=5*2^(6k+1), and set y=3*2^(6k+1), for then x^2-y^2=2^(12k+6), while x^3-y^3=49*2^(18k+4); the smallest non-trivial solutions are {10,6}

Small x={10,640,40960,2621440,167772160..}, small y={6,384,24576,1572864,100663296..}

Posted by broll on 2011-05-09 05:59:43