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)

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

Puzzle Answer

Comment 6 of 6 |

All prime numbers greater than 3 are either 1, 5, 7, or 11 mod 12.

The square of each of these remainders comes out to be a multiple of 12, plus 1. By adding 14, we are essentially adding 2 to the remainder, leading to a remainder of 3 for all primes greater than 3. That is:

5 * 5 + 14 = 25 + 14 = 39 =3 * 12 + 3

7 * 7 + 14 = 49 + 14 = 63 = 5 * 12 + 3

11 * 11 + 14 = 121 + 14 = 135 = 11 * 12 + 3

13*13 +14 = 169 +14 =183 = 15*12+3

Posted by K Sengupta on 2024-05-30 00:28:03

Please log in:

Login:
Password:
Remember me:

Sign up! \| Forgot password

Search:

Search body:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (0)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info