Thue’s lemma

Let p be a prime numberMathworldPlanetmath of the form 4k+1 . Then there are two unique integers a and b with 0<a<b such that p=a2+b2. Additionally, if a number p can be written in as the sum of two squares in 2 different ways (i.e. p=a2+b2 and p=c2+d2 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