[math-fun] 33 as sum of 3 integer cubes
33=8866128975287528^3+(-8778405442862239)^3+(-2736111468807040)^3 found by Timothy Browning communicated on Quora by Alon Amit
Perhaps I should have given some context before just posting 33=8866128975287528^3+(-8778405442862239)^3+(-2736111468807040)^3 expressing 33 as the sum of 3 integer cubes. For that see the first paragraph of Bjorn Poonen's 2008 paper Undecidability in number theory which is online (as a viewable pdf file), here: http://www-math.mit.edu/~poonen/papers/h10_notices.pdf On Fri, Mar 8, 2019 at 5:44 PM James Buddenhagen <jbuddenh@gmail.com> wrote:
33=8866128975287528^3+(-8778405442862239)^3+(-2736111468807040)^3 found by Timothy Browning communicated on Quora by Alon Amit
correction: 33=8866128975287528^3+(-8778405442862239)^3+(-2736111468807040)^3 was found by Andrew R. Booker (not by Timothy Browning as I stated above). His paper is here: https://people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf Also, D.R. Heath-Brown has conjectured that if k is not +-4 mod 9 then there are infinitely many solutions in integers to x^3 + y^3 + z^3 = k. Apparently this conjecture is thought to be true by Booker and (some?) others familiar with the problem. On Fri, Mar 8, 2019 at 5:44 PM James Buddenhagen <jbuddenh@gmail.com> wrote:
33=8866128975287528^3+(-8778405442862239)^3+(-2736111468807040)^3 found by Timothy Browning communicated on Quora by Alon Amit
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James Buddenhagen