## Experimental Mathematics

### 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

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