Quadratic forms representing all primes

DeBenedetto, Justin

doi:10.2140/involve.2014.7.619

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Quadratic forms representing all primes

Justin DeBenedetto

Vol. 7 (2014), No. 5, 619–626

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.

Keywords

quadratic forms, number theory, prime number

Mathematical Subject Classification 2010

Primary: 11E25

Secondary: 11E20

Milestones

Received: 3 May 2013

Revised: 1 October 2013

Accepted: 22 December 2013

Published: 1 August 2014

Communicated by Kenneth S. Berenhaut

Authors

Justin DeBenedetto
Department of Mathematics Wake Forest University 127 Manchester Hall Box 7388 Winston-Salem, NC 27109 United States

Vol. 7, No. 5, 2014