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 April 16th, 2009, 09:13 AM #1 Senior Member   Joined: Nov 2007 Posts: 633 Thanks: 0 Pythagorean primes and Wilson Hi, Here is a new statement. p>3 April 16th, 2009, 04:31 PM #2 Senior Member   Joined: Oct 2008 Posts: 215 Thanks: 0 Re: Pythagorean primes and Wilson Yes. It is easy to get the solution. But it is still difficult to use it for primality test April 16th, 2009, 04:41 PM #3 Senior Member   Joined: Nov 2007 Posts: 633 Thanks: 0 Re: Pythagorean primes and Wilson Step by step you can solve the problem. The 2 statements have some consequences anyway. Example : If p is pythagorean it divide abs(P(o)-P(e)) If p is not pythagorean then P(e) which is equal to m!*2^m will give you a solution for the diophantine equation : a*p = m!*2m + 1 (or p-1) and so on April 16th, 2009, 04:51 PM #4 Senior Member   Joined: Oct 2008 Posts: 215 Thanks: 0 Re: Pythagorean primes and Wilson I think P(o)=P(e) (mod p) for all p in the format of 4k+1 not only Pythagorean primes April 16th, 2009, 04:57 PM   #5
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Re: Pythagorean primes and Wilson

Quote:
 Originally Posted by duz I think P(o)=P(e) (mod p) for all p in the format of 4k+1 not only Pythagorean primes
But at my knowledge (maybe am I wrong) a Pythagorean prime is a prime of the form of 4k+1.

http://www.research.att.com/~njas/seque ... o=Chercher April 16th, 2009, 05:03 PM #6 Senior Member   Joined: Oct 2008 Posts: 215 Thanks: 0 Re: Pythagorean primes and Wilson Yes. I know the Pythagorean primes are prime of form 4k+1. But the problem is that the first equivalence holds for all integers in the form 4k+1 (so it holds for pythagorean primes too). So the result is so trival April 16th, 2009, 05:15 PM   #7
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Re: Pythagorean primes and Wilson

Quote:
 Originally Posted by duz Yes. I know the Pythagorean primes are prime of form 4k+1. But the problem is that the first equivalence holds for all integers in the form 4k+1 (so it holds for pythagorean primes too). So the result is so trival
If an integer is not prime how the statement is going to hold?
I did not say that P(e) mod p is different from zero.
It is trivial to signal it.

Example 93 = 4*23 +1 =3*31

P(o)=3*5*7*..*31*.....*45 mod (93)=0
P(e)=2*4*6*...........*46 = different from zero because 2*31=61>46. Tags primes, pythagorean, wilson Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post agustin975 Number Theory 15 April 8th, 2013 05:44 AM Scooter Number Theory 9 October 21st, 2010 12:10 PM Barbarel Number Theory 7 October 26th, 2009 01:18 PM Ben92 Number Theory 1 July 15th, 2009 11:01 AM mathsss22 Number Theory 1 November 8th, 2008 07:26 PM

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