My Math Forum Trying to make history, or at least understand primes better
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February 13th, 2009, 09:34 AM   #2
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Re: Trying to make history, or at least understand primes better

Quote:
 Originally Posted by approx obviously p^2-4c must be a perfect square
p^2 + 4c, I think.

Working mod 9, you can show that 9 | c, thus k_2 >= 2. I imagine similar things can be shown mod other prime powers. Have you tried this approach?

 February 18th, 2009, 06:50 PM #3 Newbie   Joined: Feb 2009 Posts: 4 Thanks: 0 Re: Trying to make history, or at least understand primes better Thank you for the idea, I should have thought of it before (actually I looked at it with 2, but not 3 or the others). Sorry I haven't had time to reply recently. I'll look into this approach, and thanks again!
 February 18th, 2009, 07:03 PM #4 Newbie   Joined: Feb 2009 Posts: 4 Thanks: 0 Re: Trying to make history, or at least understand primes better Okay, I can see that p^2, being odd and a square, must be congruent to 1 mod 6, and that p^2+4c, also being an odd square, must be congruent to 1 mod 6, but that just tells me that 4c is a multiple of 6, I'm still working on it but I don't get the "multiple of 9" part...
 February 18th, 2009, 08:52 PM #5 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Trying to make history, or at least understand primes better List the squares mod 9.
 February 24th, 2009, 05:23 PM #6 Newbie   Joined: Feb 2009 Posts: 4 Thanks: 0 disagree x^2+13x-48=0 has integer roots, yet 9 does not divide 48.
 February 24th, 2009, 06:10 PM #7 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Trying to make history, or at least understand primes better Oops, then? Maybe I switched from working mod 9 to mod 8 at some point.

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