Differences

rgoudie
Posers and Puzzles 03 Jun '04 01:52
1. 03 Jun '04 01:52
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.
2. 03 Jun '04 09:371 edit
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?
3. royalchicken
CHAOS GHOST!!!
03 Jun '04 17:10
1^3 - 0^3 = 1^2

1^2 - 0^2 = 1^3
4. 03 Jun '04 17:29
Originally posted by royalchicken
1^3 - 0^3 = 1^2

1^2 - 0^2 = 1^3
Yes; but that is quite trivial. Maybe we should add the requirement that there is no zero involved?
5. 04 Jun '04 00:05
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.
6. 04 Jun '04 07:48
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 ðŸ˜€
7. Acolyte