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        riddles >> medium >> Three forever
        
(Message started by: BenVitale on Aug 23^rd, 2011, 4:46pm)

Title: Three forever
Post by BenVitale on Aug 23^rd, 2011, 4:46pm

On perplexus (http://perplexus.info/show.php?pid=7080) I posted an answer to

Choose a prime number greater than 3.
Multiply it by itself and add 14.
Divide by 12 and write down the remainder.
It will always be 3.

WHY?

I received no feedback. Is my answer wrong? If so, why?

Title: Re: Three forever
Post by Grimbal on Aug 24^th, 2011, 2:20am

A prime p>3 is odd and not divisible by 3.

Modulo 12 p can only be 1, 5, 7, 11.

The remainder modulo 12 of p*p+14 depends only on the class of p modulo 12. So if the formula works for these 4 cases, it works for all odd numbers not divisible by 3.

Title: Re: Three forever
Post by pex on Aug 24^th, 2011, 3:21am

on 08/23/11 at 16:46:59, BenVitale wrote:

I received no feedback. Is my answer wrong? If so, why?

No, your answer seems perfectly valid. The reason you received no feedback is probably that you were the fifth person to post basically the same solution, in a thread that had been dead for almost a year.