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JEE Main & Advanced Mathematics Binomial Theorem and Mathematical Induction Question Bank Mathematical induction and Divisibility problems

  • question_answer
    If p is a prime number, then \[{{n}^{p}}-n\] is divisible by p when n is a

    A) Natural number greater than 1

    B) Irrational number

    C) Complex number

    D) Odd number

    Correct Answer: A

    Solution :

      \[{{n}^{p}}-n\] is divisible by p for any natural number greater than 1. It is Fermet's theorem. Trick: Let \[n=4\] and \[p=2\] Then\[{{(4)}^{2}}-4=16-4=12\], it is divisible by 2. So, it is true for any natural number greater than 1.


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