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?
Originally posted by pidermanI take the natural numbers or N to exclude zero - after all zero was not thought to be a number at all in the past, so it's hardly 'natural' from a human perspective, and it's not really a counting number either, unless you're a computer scientist. If I need to write 'the natural numbers with zero' I write Z subscript(at least 0) (looks better with the appropriate symbols). I suppose I could use Z subscript(strictly greater than 0) instead of N, as that would also be unambiguous.
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 😀