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A158794
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Multiples of 4 which are not the sum of seven nonnegative cubes.
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0
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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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]
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CROSSREFS
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KEYWORD
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bref,fini,full,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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