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# Is this conjecture regarding primes true?

### #1

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?

### #2

Posted 02 April 2013 - 06:21 PM Best Answer

Past prime, actually.

### #3

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?

### #4

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

### #5

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.**

Past prime, actually.

### #6

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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