Representations of Positive Definite Senary Integral Quadratic Forms by a Sum of Squares Original Research Article

As a generalization of the famous four square theorem of Lagrange, it was proved that every positive definite integral quadratic form ofnvariables is represented by the sun ofn+3 squares for 1less-than-or-equals, slantnless-than-or-equals, slant5. In this paper, we prove that every positive definite integral quadratic form of six variables that can be represented by a sum of squares is represented by the sum of ten squares, no less.