Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: question about congruence classes
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
manontheclaphamomnibus

Posts: 31
Registered: 11/12/12
question about congruence classes
Posted: Jan 21, 2013 8:42 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

This following must obviously be too simple, but if someone can explain what it misses, I'd be very grateful.

If there are only finitely many pairs (n, n+2), both prime, then from the apparently infinitely many numbers x such that x is

neither [0]mod2 nor [0]mod2,
nor [0]mod3 nor [1]mod3,
nor [0]mod5 nor [3]mod5....
nor [0]modp nor [p-2](modp for all p < sqrt(x + 1)),

then above a certain size, either the seeming inductive step for filtering all candidate numbers x by the two requirements modulo the next additional prime breaks down, or else some extra condition begins to hold.

Either way, somehow even if infinitely many x remain satisfying the conditions for each specific p_i from then on, none of them after this point need be small enough to ensure any longer that infinitely many x meet these conditions for all values of p < sqrt(x + 1) in general? Is this the main problem with trying to show this?

Thanks!



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.