-
Recent Posts
Archives
- March 2023
- January 2023
- May 2020
- April 2020
- March 2020
- June 2018
- July 2016
- June 2016
- May 2016
- March 2015
- February 2015
- January 2015
- December 2014
- December 2013
- November 2013
- July 2013
- June 2013
- May 2013
- March 2013
- February 2013
- January 2013
- December 2012
- November 2012
- October 2012
- September 2012
- August 2012
- April 2012
- March 2012
- February 2012
- January 2012
- December 2011
- November 2011
- October 2011
Categories
Meta
Pages
Tag Archives: quadratic residues
Quadratic Residues – Part IV (Applications)
Let p be an odd prime and g be a primitive root modulo p. Given any a which is not a multiple of p, we can write for some r. We mentioned at the end of the last section that a is a square if … Continue reading
Quadratic Residues – Part III
Ok, here’s the third installation. Getting a little tired of repeatedly saying “a is/isn’t a square mod p“, we introduce a new notation. Definition. Let p be an odd prime and a be an integer coprime to p. The Legendre symbol … Continue reading
Posted in Notes
Tagged intermediate, legendre symbol, notes, number theory, quadratic residues
Leave a comment
Quadratic Residues – Part II
Recall what we’re trying to do here: to show that if p > 2 is prime and a is not a square modulo p, then . As mentioned at the end of the previous part, we will need… Primitive Roots Again, let … Continue reading
Quadratic Residues – Part I
[ Background required : modular arithmetic. Seriously. ] Warning: many of the proofs for theorems will be omitted in this set of notes, due to the length of the proofs. The basic question we’re trying to answer in this series … Continue reading
Mathematics and Such 