Geometry of numbers approach to small solutions to the extended Legendre equation
Nunley, Laura Michelle
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In this paper, the reader will be introduced to quadratic forms, lattices, and the Legendre Equation. We will extend Legendre’s equation to multiple variables, and in the cases where n >= 4, attempt to extend Cochrane and Mitchell’s proof of the existence of solutions. It will be proven that the proof does not hold for more than three variables.