Let p be an odd prime number. Prove the following facts about squares modulo p. Use primitive
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Let p be an odd prime number. Prove the following facts about squares modulo p. Use primitive roots to prove a) to d)
(a) The number of quadratic residues modulo p is the same as the number of nonquadratic residues.
(b) The product of two quadratic residues is again a quadratic residue.
(c) The product of two nonquadratic residues is a quadratic residue.
(d) The product of a quadratic residue and nonquadratic residue is a nonquadratic residue.
(e) Use the previous facts to justify that the Legendre Symbol satisfies (ab/p) = (a/p) (b/p) for any integers a, b.
Related Book For
Introduction to Algorithms
ISBN: 978-0262033848
3rd edition
Authors: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest
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