781hw5 - investigate what proportion of residues mod p are...

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18.781, Fall 2007 Problem Set 5 Due: FRIDAY, October 12 1. Complete the following problems from Niven-Zuckerman-Montgomery (henceforth NZM): Read section 2.11 and complete the following problems: NZM 2.11: 1, 6, 11 NZM 3.1: 5, 7, 10, 12, 14, 17, 18, 20 2. PARI PROGRAM OF THE WEEK: We know that quadratic residues mod p are always easy to find (e.g. 1 mod p ), but what about non-residues? First, write a PARI program to
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Unformatted text preview: investigate what proportion of residues mod p are quadratic residues vs. non-residues. Can you explain or prove your answer? What about the smallest quadratic non-residue? How big is it, in terms of p ? Write a PARI program to test how large the smallest quadratic NON-residue is. Given any N , do you think you can find a prime p with the smallest quadratic NON-residue > N ?...
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