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Does anyone know if there is a conjectural characterization of those numbers which can be expressed as the sum of three cubes? The article mentions not being co
by kevinventullo 8y ago
Does anyone know if there is a conjectural characterization of those numbers which can be expressed as the sum of three cubes? The article mentions not being congruent to 4 or 5 mod 9 is a necessary condition. Is it (conjecturally) sufficient?
- deleted 8y ago[deleted]
- jhncls 8y agoIn the Numberphile video it is conjectured that there are infinitely many solutions for all those numbers, but that solutions are very sparse. The smallest solution for 42 might involve very high numbers.
- kevinventullo 8y agoThanks! It seems they mentioned this in the article as well: "A major result would be to prove the conjecture that k = x³ + y³ + z³ has infinitely many solutions for every whole number k, except those k that have a remainder of 4 or 5 after being divided by 9."