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Three forever (Posted on 2010-09-30) Difficulty: 2 of 5
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
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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