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%I #11 Feb 08 2022 08:01:12
%S 212,364,420,428
%N Multiples of 4 which are not the sum of seven nonnegative cubes.
%C Boklan and Elkies: It is conjectured that every integer N>454 is the sum of seven nonnegative cubes. We prove the conjecture when N is a multiple of 4.
%C Elkies [2010]: It is conjectured that every integer N>454 is the sum of seven nonnegative cubes. We prove the conjecture when N is congruent to 2 mod 4. This result, together with a recent proof for 4|N, shows that the conjecture is true for all even N. - _Jonathan Vos Post_, Sep 22 2010
%D U. V. Linnik: On the representation of large numbers as sums of seven cubes. Rec. Math. [=Mat. Sbornik] N.S. 12(54) (1943), 218-224.
%D L. E. Dickson: All integers except 23 and 239 are the sums of 8 cubes. Bull. Amer. Math. Soc. 45 (1939), 588-591.
%H E. Waring: Meditationes Algebraicae [3rd ed. (1782)]: an English translation of the work of Edward Waring, edited and translated from the Latin by Dennis Weeks. Providence, RI: Amer. Math. Soc., 1991. [<a href="http://www.ams.org/mathscinet-getitem?mr=1146921">MR1146921</a>]
%H Kent D. Boklan and Noam D. Elkies, <a href="http://arxiv.org/abs/0903.4503"> Every multiple of 4 except 212, 364, 420, and 428 is the sum of seven cubes</a>, arXiv:0903.4503, Mar 26, 2009.
%H Noam D. Elkies, <a href="http://arxiv.org/abs/1009.3983">Every even number greater than 454 is the sum of seven cubes</a>, Sep 21, 2010. [From _Jonathan Vos Post_, Sep 22 2010]
%Y Cf. A000578, A003072, A003325, A003327, A003328, A003329, A057907, A122730.
%Y Subsequence of A018888. - _Charles R Greathouse IV_, Apr 16 2010
%K bref,fini,full,nonn
%O 1,1
%A _Jonathan Vos Post_, Mar 26 2009
%E Definition corrected by _Jonathan Sondow_, Mar 14 2014
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