A158794 Multiples of 4 which are not the sum of seven nonnegative cubes.

212, 364, 420, 428

Offset: 1

Author

Jonathan Vos Post, Mar 26 2009

Keywords

• bref
• fini
• full
• nonn

Comments

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.

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

References

• 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.
• L. E. Dickson: All integers except 23 and 239 are the sums of 8 cubes. Bull. Amer. Math. Soc. 45 (1939), 588-591.

Links

• 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. [MR1146921]
• Kent D. Boklan and Noam D. Elkies, Every multiple of 4 except 212, 364, 420, and 428 is the sum of seven cubes, arXiv:0903.4503, Mar 26, 2009.
• Noam D. Elkies, Every even number greater than 454 is the sum of seven cubes, Sep 21, 2010. [From _Jonathan Vos Post_, Sep 22 2010]

Crossrefs

Cf. A000578, A003072, A003325, A003327, A003328, A003329, A057907, A122730.

Subsequence of A018888. - Charles R Greathouse IV, Apr 16 2010

Extensions

Definition corrected by Jonathan Sondow, Mar 14 2014