Involve: A Journal of Mathematics

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

Quadratic forms representing all primes

Justin DeBenedetto

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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

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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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

quadratic forms number theory prime number


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

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