Thue’s lemma

Let $p$ be a prime number of the form $4k+1$ . Then there are two unique integers $a$ and $b$ with such that $p=a^2+b^2$. Additionally, if a number $p$ can be written in as the sum of two squares in 2 different ways (i.e. $p=a^2+b^2$ and $p=c^2+d^2$ with the two sums being different), then the number $p$ is composite.

Title	Thue’s lemma
Canonical name	ThuesLemma
Date of creation	2013-03-22 13:19:05
Last modified on	2013-03-22 13:19:05
Owner	mathcam (2727)
Last modified by	mathcam (2727)
Numerical id	8
Author	mathcam (2727)
Entry type	Theorem
Classification	msc 11A41
Related topic	RepresentingPrimesAsX2ny2