Vol. 7, No. 5, 2014

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ISSN: 1944-4184 (e-only)
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Quadratic forms representing all primes

Justin DeBenedetto

Vol. 7 (2014), No. 5, 619–626
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