17 votes

42 can be written as the sum of three cubes, which was the last remaining unsolved case under 100

3 comments

  1. [3]
    Algernon_Asimov
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    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.

    1. [2]
      Comment deleted by author
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      1. Algernon_Asimov
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        Because it's cheating! (I don't know. It just surprised me.)

        And why wouldn't you be allowed to use negative numbers in the cubed case?

        Because it's cheating!

        (I don't know. It just surprised me.)

        2 votes
    2. [2]
      Comment deleted by author
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      1. Algernon_Asimov
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        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.

        1 vote