# hw5 - p while if p â‰ 3(mod 4 then-a is a quadratic...

This preview shows page 1. Sign up to view the full content.

Math 465 Problem Set 5 Due Friday, March 7, 2008 1. Find all quadratic residues and non-residues modulo 13. 2. Use Euler’s Criterion to evaluate the following Legendre symbols: (a) ( 11 23 ) (b) ( - 6 11 ) 3. Use Gauss’s Lemma to evaluate the following Legendre symbols: (a) ( 12 23 ) (b) ( - 5 11 ) 4. Let p be an odd prime and a be a quadratic residue of p . Prove that if p 1 (mod 4), then - a is also a quadratic residue of
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: p , while if p â‰¡ 3 (mod 4), then-a is a quadratic non-residue of p . 5. Prove that if p is an odd prime and a, b are integers with ( a, p ) = 1, then p X n =1 Â± an + b p Â² = 0 . (Hint: show that { an + b | ( a, p ) = 1 , n = 1 , 2 , . . . , p } is a complete residue system modulo p , and that âˆ‘ p x =1 Â³ x p Â´ = 0.) 1...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business â€˜17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. Itâ€™s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania â€˜17, Course Hero Intern

• The ability to access any universityâ€™s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLAâ€™s materials to help me move forward and get everything together on time.

Jill Tulane University â€˜16, Course Hero Intern