Let p be a prime. Determine all positive integers n for which the following condition is satisfied for all integers x. Condition: If x^{n} - 1 is divisible by p, then it is also divisible by p^{2}.
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What have you tried so far? What formulas or rules are you allowed to use? Where are you stuck?Let p be a prime. Determine all positive integers n for which the following condition is satisfied for all integers x. Condition: If x^{n} - 1 is divisible by p, then it is also divisible by p^{2}.
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What have you tried so far? What formulas or rules are you allowed to use? Where are you stuck?Let p be a prime. Determine all positive integers n for which the following condition is satisfied for all integers x. Condition: If x^{n} - 1 is divisible by p, then it is also divisible by p^{2}.
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