The 15 theorem, also called the Conway-Schneeberger Fifteen Theorem, is a result in number theory proved by John H. Conway and W. A. Schneeberger in 1993. It states that a positive definite quadratic form arising from an integer matrix represents every positive integer, provided it represents every positive integer up to 15. Conway and Schneeberger did not publish their original proof because Manjul Bhargava later found a simpler one, published in 2000. Conway also conjectured an analogous statement for integral quadratic forms with the constant 15 replaced by 290; Bhargava and Jonathan Hanke produced a 2011 preprint proving this 290 conjecture, though it remains unpublished. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementThe 15 theorem states that if a positive definite quadratic form arising from an integer matrix represents all positive integers up to 15, then it represents all positive integers. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Source 15 and 290 theorems (Wikipedia)
Proved By
Source 15 and 290 theorems (Wikipedia)
Sources
1. 15 and 290 theorems (Wikipedia)
Introduction
states that if a positive definite quadratic form arising from an integer matrix represents all positive integers up to 15, then it represents all positive integers
Introduction [proof-year]
proved by John H. Conway and W. A. Schneeberger in 1993
Proved By: John Conway, Lead sentence, attribution
proved by John H. Conway and W. A. Schneeberger in 1993
In Branch: Number Theory, Lead section
arising from an integer matrix represents all positive integers up to 15, then it represents all positive integers.
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