perplexus.info :: Tricks : Three forever

Three forever (Posted on 2010-09-30)

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?

No Solution Yet Submitted by Ady TZIDON

Rating: 2.7500 (4 votes)

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solution

Comment 5 of 5 |

A prime p has to be 1 or 2 mod 3,

and this implies that p^2 = 1 mod 3.

Also, p has to be 1 or 3 mod 4,

and this implies that p^2 = 1 mod 4.

So, p^2 = 1 mod 12, and so p^2 + 14 = 15 = 3 mod 12

Posted by BenVitale on 2011-08-22 03:39:26

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