Let Q(x) = Q(x_1, x_2, ..., x_n) be an integer-valued n-ary quadratic form, i.e., a polynomial with integer coefficients which satisfies Q(x)>0 for real x!=0. Then Q(x) can be represented by Q(x) = x^T A x, where A = 1/2 (d^2 Q(x))/(dx_i dx_j) is a positive symmetric matrix. If A has positive entries, then Q(x) is called an integer-matrix form. Conway et al. (1997) have proven that, if a positive integer-matrix quadratic form represents each of 1, 2, 3, 5, 6, 7, 10, 14, and 15, then it represents all positive integers.
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