A theorem due to Conway *et al. *(1997) which states that, if a Positive definite Quadratic Form with
integral 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.

**References**

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.

© 1996-9

1999-05-26