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6 replies to this topic

#1 bonanova

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Posted 18 February 2008 - 10:09 AM

Prove or disprove:
If p is a prime number > 3, then p2-1 is divisible by 24.
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#2 Aatif

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Posted 18 February 2008 - 10:57 AM

Prove or disprove:
If p is a prime number > 3, then p2-1 is divisible by 24.


I love primes :)
Spoiler for Primal Fear

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#3 110011

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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.
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#4 Aatif

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Posted 22 February 2008 - 05:25 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.

No. 51 .. No. The definition of "divisible" given by www.dictionary.com is:

di·vis·i·ble /dɪˈvɪzəbəl/ Pronunciation Key - [di-viz-uh-buhl]
–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, p2-1 is exactly divisible by 24.

I rest my case.
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#5 bonanova

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Posted 22 February 2008 - 05:52 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.

By definition of prime number the square of any prime number is divisible by itself, the prime number and 1.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 Duh Puck

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Posted 24 February 2008 - 03:08 PM

p2-1 = (p+1)(p-1)

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!
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#7 storm

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Posted 25 February 2008 - 02:56 AM

Spoiler for The proof

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