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2014 Quadratic forms representing all primes
Justin DeBenedetto
Involve 7(5): 619-626 (2014). DOI: 10.2140/involve.2014.7.619

Abstract

Building on the method used by Bhargava to prove “the fifteen theorem”, we show that every integer-valued positive definite quadratic form which represents all prime numbers must also represent 205. We further this result by proving that 205 is the smallest nontrivial composite number which must be represented by all such quadratic forms.

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Justin DeBenedetto. "Quadratic forms representing all primes." Involve 7 (5) 619 - 626, 2014. https://doi.org/10.2140/involve.2014.7.619

Information

Received: 3 May 2013; Revised: 1 October 2013; Accepted: 22 December 2013; Published: 2014
First available in Project Euclid: 20 December 2017

zbMATH: 1295.11032
MathSciNet: MR3245839
Digital Object Identifier: 10.2140/involve.2014.7.619

Subjects:
Primary: 11E25
Secondary: 11E20

Keywords: number theory , prime number , Quadratic forms

Rights: Copyright © 2014 Mathematical Sciences Publishers

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Vol.7 • No. 5 • 2014
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