I know about this family of number problems: express X as a sum of two cubes; express Y as a sum of three squares; and so on. But the versions I've seen all assume that the numbers being squared...
I know about this family of number problems: express X as a sum of two cubes; express Y as a sum of three squares; and so on. But the versions I've seen all assume that the numbers being squared and cubed (etc) are whole positive integers. I didn't know people were allowed to use negative numbers. That feels like cheating.
Yes, I know that there would be some values that are impossible to be created by a sum of three cubed integers without using negative integers. To me, that's the point: not all numbers can be...
Yes, I know that there would be some values that are impossible to be created by a sum of three cubed integers without using negative integers. To me, that's the point: not all numbers can be formulated in this way, which means the numbers that can be so formulated are rare and therefore special. I never thought this was supposed to be a universal property of all numbers. I thought it was supposed to be a special property of only some numbers.
I know about this family of number problems: express X as a sum of two cubes; express Y as a sum of three squares; and so on. But the versions I've seen all assume that the numbers being squared and cubed (etc) are whole positive integers. I didn't know people were allowed to use negative numbers. That feels like cheating.
Because it's cheating!
(I don't know. It just surprised me.)
Yes, I know that there would be some values that are impossible to be created by a sum of three cubed integers without using negative integers. To me, that's the point: not all numbers can be formulated in this way, which means the numbers that can be so formulated are rare and therefore special. I never thought this was supposed to be a universal property of all numbers. I thought it was supposed to be a special property of only some numbers.