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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.

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