Let p be a prime....

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

Let p be a prime....

Postby circumference on Sat Apr 13, 2013 8:28 am

Let p be a prime. Determine all positive integers n for which the following condition is satisfied for all integers x. Condition: If xn - 1 is divisible by p, then it is also divisible by p2.
Help! :confused:
Last edited by circumference on Sat Apr 13, 2013 1:50 pm, edited 1 time in total.
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Postby stapel_eliz on Sat Apr 13, 2013 11:46 am

The image doesn't appear to be loading within your post, for some reason. Since it's only text, it might be helpful to type it out, so people can see what you're asking.

The author of the exercise wrote:Let p be a prime. Determine all positive integers n for which the following condition is satisfied for all integers x. Condition: If xn - 1 is divisible by p, then it is also divisible by p2.

What have you tried so far? What formulas or rules are you allowed to use? Where are you stuck?

Please be complete, so the volunteers can see where you're having difficulty. Thank you! :wink:
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Re: Let p be a prime....

Postby circumference on Sat Apr 13, 2013 1:49 pm

stapel_eliz wrote:The image doesn't appear to be loading within your post, for some reason. Since it's only text, it might be helpful to type it out, so people can see what you're asking.

The author of the exercise wrote:Let p be a prime. Determine all positive integers n for which the following condition is satisfied for all integers x. Condition: If xn - 1 is divisible by p, then it is also divisible by p2.

What have you tried so far? What formulas or rules are you allowed to use? Where are you stuck?

Please be complete, so the volunteers can see where you're having difficulty. Thank you! :wink:


Thanks!
You can use any formulas, theorems and other stuff.
I proved that if such n exists, p|n and n is odd, but I am stuck there.
Can you help me?
Thanks in advance! :clap:
circumference
 
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