#### Title

A cubic analogue of the jacobsthal identity

#### Document Type

Article

#### Publication Date

4-1-2011

#### Abstract

It is well known that if p is a prime such that p = 1 (mod 4), then p can be expressed as a sum of two squares. Several proofs of this fact are known and one of them, due to E. Jacobsthal, involves the identity p = x2 + y2, with x and y expressed explicitly in terms of sums involving the Legendre symbol. These sums are now known as the Jacobsthal sums. In this short note, we prove that if p = 1 (mod 6), then 3p = u2 + uv + v 2 for some integers u and v using an analogue of Jacobsthal 's identity. © THE MATHEMATICAL ASSOCIATION OF AMERICA.

#### Publication Source (Journal or Book title)

American Mathematical Monthly

#### First Page

316

#### Last Page

326

#### Recommended Citation

Chan, H., Long, L., & Yang, Y.
(2011). A cubic analogue of the jacobsthal identity.* American Mathematical Monthly**, 118* (4), 316-326.
https://doi.org/10.4169/amer.math.monthly.118.04.316