Involve: A Journal of Mathematics

  • Involve
  • Volume 7, Number 5 (2014), 619-626.

Quadratic forms representing all primes

Justin DeBenedetto

Full-text: Open access

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.

Article information

Source
Involve, Volume 7, Number 5 (2014), 619-626.

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

Permanent link to this document
https://projecteuclid.org/euclid.involve/1513733721

Digital Object Identifier
doi:10.2140/involve.2014.7.619

Mathematical Reviews number (MathSciNet)
MR3245839

Zentralblatt MATH identifier
1295.11032

Subjects
Primary: 11E25: Sums of squares and representations by other particular quadratic forms
Secondary: 11E20: General ternary and quaternary quadratic forms; forms of more than two variables

Keywords
quadratic forms number theory prime number

Citation

DeBenedetto, Justin. Quadratic forms representing all primes. Involve 7 (2014), no. 5, 619--626. doi:10.2140/involve.2014.7.619. https://projecteuclid.org/euclid.involve/1513733721


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References

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