Involve: A Journal of Mathematics
- Volume 7, Number 5 (2014), 619-626.
Quadratic forms representing all primes
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.
Involve, Volume 7, Number 5 (2014), 619-626.
Received: 3 May 2013
Revised: 1 October 2013
Accepted: 22 December 2013
First available in Project Euclid: 20 December 2017
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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