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Is this conjecture regarding primes true?


Best Answer Prime, 02 April 2013 - 06:21 PM

Spoiler for easy

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#1 BMAD

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Posted 02 April 2013 - 05:49 PM

For every prime number (p) greater than 3, there exists a natural number (n) such that

 

p^2 = 12(n)-11.  Can you provide a counterexample? Else, can you prove it?


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#2 Prime

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Posted 02 April 2013 - 06:21 PM   Best Answer

Spoiler for easy


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Past prime, actually.


#3 dark_magician_92

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Posted 02 April 2013 - 06:31 PM

For every prime number (p) greater than 3, there exists a natural number (n) such that

 

p^2 = 12(n)-11.  Can you provide a counterexample? Else, can you prove it?

Spoiler for


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#4 BMAD

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Posted 02 April 2013 - 06:37 PM

I never know when to use Q.E.D. vs Without loss of generality, is there a difference or is it just a style thing?

Spoiler for easy


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#5 Prime

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Posted 02 April 2013 - 07:07 PM

I never know when to use Q.E.D. vs Without loss of generality, is there a difference or is it just a style thing?

Spoiler for easy

"Q.E.D"  means "which had to be demonstrated" and typically refers to the concluding statement(s) of a proof.

"WLOG" points to a relation between statements/formulas. Like, if it is good for Goose than without loss of generality it must be good for Gender. Or, let's say, in an induction proof: if the rule holds for a randomly chosen number WLOG it must hold for any other number. Q.E.D.


Edited by Prime, 02 April 2013 - 07:09 PM.

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Past prime, actually.


#6 witzar

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Posted 03 April 2013 - 11:08 PM

I never know when to use Q.E.D. vs Without loss of generality, is there a difference or is it just a style thing?

WLOG often starts the proof while QED ends it.

You can decide which one to use on the basis of your progress with the proof ;)


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