Proof of Sum of Two Squares Theorem using Gaussian Integers

Authors

  • Ayush Jain The Shir Ram School Aravali
  • Joy Hamlin Department of Mathematics, PhD student, Rutgers University

DOI:

https://doi.org/10.47611/jsrhs.v12i4.5562

Keywords:

Gaussian Integers, Number Theory, Sum of Two Squares

Abstract

I provide a proof of Fermat’s Sum of Two Squares theorem using Gaussian Integers. The theorem characterizes the integers that can be represented as a sum of two integer squares: n = a2 + b2 for some n, a, b ∈ Z.  Few authors have provided proof of the theorem using Thu’s Lemma and Fermat’s Little Theorem. This paper uses Gaussian integers to prove the extended theorem.

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References or Bibliography

J. Bhaskar. Sum of two squares. REU Papers, 2008. URL https://math.uchicago.edu/~may/ VIGRE/VIGRE2008/REUPapers/Bhaskar.pdf.

K. Conrad. The gaussian integers. URL https://kconrad.math.uconn.edu/blurbs/ ugradnumthy/Zinotes.pdf.

C. Londahl. Lecture on sums of squares. 2011. URL https://carllondahl.files.wordpress. com/2011/05/sumsofsquares1.pdf.

J. Stillwell. Introduction to Theory of Algebraic Integers by Richard Dedekind. Cambridge Mathematical Library, Cambridge University Press, 1996.

Published

11-30-2023

How to Cite

Jain, A., & Hamlin, J. (2023). Proof of Sum of Two Squares Theorem using Gaussian Integers. Journal of Student Research, 12(4). https://doi.org/10.47611/jsrhs.v12i4.5562

Issue

Vol. 12 No. 4 (2023)

Section

HS Research Articles

Copyright (c) 2023 Ayush Jain; Joy Hamlin

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