Pythagorean Primes and Palindromic Continued Fractions

Authors

Arthur T. Benjamin, Harvey Mudd CollegeFollow
Doron Zeilberger, Rutgers University - Camden

Document Type

Article

Department

Mathematics (HMC)

Publication Date

12-2005

Abstract

In this note, we prove that every prime of the form 4m + 1 is the sum of the squares of two positive integers in a unique way. Our proof is based on elementary combinatorial properties of continued fractions. It uses an idea by Henry J. S. Smith ([3], [5], and [6]) most recently described in [4] (which provides a new proof of uniqueness and reprints Smith's paper in the original Latin). Smith's proof makes heavy use of nontrivial properties of determinants. Our purely combinatorial proof is self-contained and elementary.

Comments

First published in INTEGERS: The Electronic Journal of Combinatorial Number Theory, vol. 5, no. 1 (December 2005), by the State University of West Georgia, Charles University, and DIMATIA.

This article is also available at http://www.integers-ejcnt.org/vol5.html.

Rights Information

© 2005 Arthur T. Benjamin

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

Benjamin, A.T., & Zeilberger, D. (2005). Pythagorean primes and palindromic continued fractions. Integers: The Electronic Journal of Combinatory Number Theory, 5(1): 1-5.