Explore BrainMass

Explore BrainMass

    Quadratic Residues

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Please see the attached file for the fully formatted problems.

    Fix a positive integer a We say that a is a quadratic residue modulo n if there exists x such that a = x^2 mod n.
    (a) Let n be an odd prime and a be a non-zero quadratic residue modulo n. Show that there are exactly two values in{O.1....,n?1} satisfying x^2=amodn.
    (b) Show that if a is an odd prime, there are exactly (n + 1)/2 quadratic residues in {0, 1...., n ? 1).
    (c) Give an example of positive integers a, n such that....

    © BrainMass Inc. brainmass.com December 24, 2021, 5:10 pm ad1c9bdddf
    https://brainmass.com/math/algebra/quadratic-residues-investigations-32548

    Attachments

    Solution Preview

    Please see the attachment.

    Proof:
    a. Suppose and (mod ), then we have (mod ). This implies that . But is an odd prime. Then we have or . This ...

    Solution Summary

    Quadratic residues are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who posted the question.

    $2.49

    ADVERTISEMENT