## Involve: A Journal of Mathematics

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

### Quadratic forms representing all primes

Justin DeBenedetto

#### 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
Revised: 1 October 2013
Accepted: 22 December 2013
First available in Project Euclid: 20 December 2017

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

#### 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

#### References

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