## Experimental Mathematics

- Experiment. Math.
- Volume 6, Issue 4 (1997), 289-292.

### Periodic Gaussian moats

#### Abstract

A question of Gordon, mistakenly attributed to Erdős, asks if one can start at the origin and walk from there to infinity on Gaussian primes in steps of bounded length. We conjecture that one can start anywhere and the answer is still no. We introduce the concept of periodic Gaussian moats to prove our conjecture for step sizes of $\sqrt 2$ and 2.

#### Article information

**Source**

Experiment. Math., Volume 6, Issue 4 (1997), 289-292.

**Dates**

First available in Project Euclid: 7 March 2003

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1047047189

**Mathematical Reviews number (MathSciNet)**

MR1606912

**Zentralblatt MATH identifier**

1115.11318

**Subjects**

Primary: 11R04: Algebraic numbers; rings of algebraic integers

Secondary: 11Y40: Algebraic number theory computations

#### Citation

Gethner, Ellen; Stark, H. M. Periodic Gaussian moats. Experiment. Math. 6 (1997), no. 4, 289--292. https://projecteuclid.org/euclid.em/1047047189