**Prove or disprove:**

If p is a prime number > 3, then p

^{2}-1 is divisible by 24.

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Guest Message by DevFuse

Started by bonanova, Feb 18 2008 10:09 AM

6 replies to this topic

Posted 18 February 2008 - 10:09 AM

If p is a prime number > 3, then p

*Vidi vici veni.*

Posted 18 February 2008 - 10:57 AM

Prove or disprove:

If p is a prime number > 3, then p^{2}-1 is divisible by 24.

I love primes

Spoiler for Primal Fear

Posted 22 February 2008 - 02:52 AM

First of all, any prime number squared is divisible by 24.

If you are talking about the dividion resulting in an integer, then that's true too.

If you are talking about the dividion resulting in an integer, then that's true too.

Posted 22 February 2008 - 05:25 AM

No. 51 .. No. The definition of "divisible" given by www.dictionary.com is:First of all, any prime number squared is divisible by 24.

If you are talking about the dividion resulting in an integer, then that's true too.

–adjective

2. Mathematics.

a. capable of being evenly divided, without remainder.

b. of or pertaining to a group in which given any element and any integer, there is a second element that when raised to the integer equals the first element.

Also, prime squared is not divisible by any other number apart from that prime number saquared, that prime number and 1.

On the other hand, p

I rest my case.

Posted 22 February 2008 - 05:52 AM

By definition of prime number the square of any prime number is divisible by itself, the prime number and 1.First of all, any prime number squared is divisible by 24.

If you are talking about the dividion resulting in an integer, then that's true too.

*Vidi vici veni.*

Posted 24 February 2008 - 03:08 PM

This is a remarkable little statement which is so simple and elegant that I can't believe I hadn't either seen it or discovered it before (I'm probably giving away my lack of math education, but that's ok). Thanks!p

^{2}-1 = (p+1)(p-1)

Posted 25 February 2008 - 02:56 AM

Spoiler for The proof

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