Fifteen Theorem

A theorem due to Conway et al. (1997) which states that, if a positive definite quadratic form with integer matrix entries represents all natural numbers up to 15, then it represents all natural numbers. This theorem contains Lagrange's four-square theorem, since every number up to 15 is the sum of at most four squares.

See also

Integer Matrix, Integer-Matrix Form, Lagrange's Four-Square Theorem, Quadratic Form

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Conway, J. H. "Re: The fifteen theorem." posting, Sept. 10, 1996.Conway, J. H.; Guy, R. K.; Schneeberger, W. A.; and Sloane, N. J. A. "The Primary Pretenders." Acta Arith. 78, 307-313, 1997.Duke, W. "Some Old Problems and New Results about Quadratic Forms." Not. Amer. Math. Soc. 44, 190-196, 1997.Petersen, I. "MathTrek: All Square." Sci. News 169, Mar. 11, 2006.

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Fifteen Theorem

Cite this as:

Weisstein, Eric W. "Fifteen Theorem." From MathWorld--A Wolfram Web Resource.

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