Abstract

Let $Q$ be a $\mathfrak{5}\times \mathfrak{5}$ symmetric matrix with integral entries and with $detQ\ne \mathfrak{0}$, but neither positive nor negative definite. We describe a probabilistic algorithm which solves the equation ${}^{t}xQx=\mathfrak{0}$ over $\mathbb{Z}$ without factoring $detQ$. The method can easily be generalized to forms of higher dimensions by reduction to a suitable subspace.

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Mathematical Subject Classification 2010

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