## Involve: A Journal of Mathematics

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

### Quadratic forms representing all primes

#### 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