# Thue’s lemma

Let $p$ be a prime number of the form $4k+1$ . Then there are two unique integers $a$ and $b$ with $0 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 ThuesLemma 2013-03-22 13:19:05 2013-03-22 13:19:05 mathcam (2727) mathcam (2727) 8 mathcam (2727) Theorem msc 11A41 RepresentingPrimesAsX2ny2