Can you find the two smallest whole numbers where the difference of their squares is a cube, and the difference of their cubes is a square?

-Ray.

Guess you forgot the word 'different'?

0^2-0^2=0^3
0^3-0^3=0^2

In case this is true, you could take 6 and 10:

10^2-6^2 = 100-36 = 64 = 8^3
10^3-6^3 = 1000-216 = 784 = 28^2

Are these the smallest?

1^3 - 0^3 = 1^2

1^2 - 0^2 = 1^3

Originally posted by royalchicken
1^3 - 0^3 = 1^2

1^2 - 0^2 = 1^3

The problem did request whole numbers. There seems to be ambiguous definitions for the set of whole numbers. In this case, the set of whole numbers was intended to be the set of positive integers.

In this case, the correct numbers are indeed 6 and 10.

-Ray.

The set of whole numbers is: -inf,...,-3,-2,-1,0,1,2,3,...,inf
Then there are the natural numbers: 0,1,2,3,...,inf
You wanted the natural numbers^+: 1,2,3,...,inf

Might be handy to remember; it stops lots of confusion 😀

Originally posted by piderman
The set of whole numbers is: -inf,...,-3,-2,-1,0,1,2,3,...,inf
Then there are the natural numbers: 0,1,2,3,...,inf
You wanted the natural numbers^+: 1,2,3,...,inf

Might be handy to remember; it stops lots of confusion 😀

Lol, piderman. You give the most trivial solution of all, assume the author meant different numbers, then make a point of someone giving the most trivial solution to your extra condition, you should be more precise in your conditions :p