Presented By: Student Number Theory Seminar - Department of Mathematics
The Fifteen Theorem
Zander Hill
We discuss a finiteness theorem of Conway and Schneeberger about quadratic forms, called the fifteen theorem. Specifically, a positive definite quadratic form over Z takes on all positive integer values if and only if it takes on the values 1,...,15. We will sketch a proof of this result, along with some less precise generalizations to a large class of similar problems.
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