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Mathematicians are interested in which natural numbers k can be expressed as a sum of three cubes. Prior to this year, it had been established that this is poss
by ocfnash 7y ago
Mathematicians are interested in which natural numbers k can be expressed as a sum of three cubes. Prior to this year, it had been established that this is possible for all k < 1000 except for the following thirteen values:
33, 42, 114, 165, 390, 579, 627, 633, 732, 795, 906, 921, 975.
Earlier this year a solution for k=33 was found [1], so 42 was the next unknown value.
[1] Brooker, A., "CRACKING THE PROBLEM WITH 33", https://people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf https://people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf
- tomd3v 7y ago> Mathematicians are interested in which natural numbers k can be expressed as a sum of three cubes. Why?
- intuitionist 7y agoThis isn’t quite right, it’s easy to show that if n is 4 or 5 (mod 9), then there are no integer solutions to a^3 + b^3 + c^3 = n. The conjecture is that the mod 9 obstruction is the only one and all other integers can be represented as the sum of 3 cubes.
- ocfnash 7y agoThanks, that was very sloppy of me!