Let $p$ be a prime number of the form $4k+1$ . Then there are two unique integers$a$ and $b$ with $0<a<b$ 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.
This is version 5 of Thue's lemma, born on 2002-12-25, modified 2005-03-18.
Object id is 3826, canonical name is ThuesLemma2.
Accessed 3564 times total.
