Let p be a prime....

[circumference]

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!

[stapel_eliz]

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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!

[circumference]

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.

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!

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!