Ch.4 24. c

Ch.4 24. c

chiph588 21 Oct 2008 17:09

I'm kind of unclear as to what this question is asking…

Re: Ch.4 24. c

andrewcschultz 21 Oct 2008 17:42

They want you to show that for any prime modulus p at least 7, there exist two numbers a and b so that

(1)

and so that both a and b are squares modulo p.

Does that help?

Last edited on 21 Oct 2008 17:43 by andrewcschultz Show more

Re: Ch.4 24. c

jensberg 21 Oct 2008 17:45

It wants you to prove that there are at least two consecutive quadratic residues mod p. That is, show that there is at least a pair n, n+1 that are quadratic residues mod p. And using part (a) is a big hint. Think about which numbers we know already are quadratic residues mod p and then see how you can use that and part (a) together. Hope that helps!