JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • question_answer
    If\[n={{2}^{p-1}}({{2}^{p}}-1)\], where \[{{2}^{p}}-1\] is a prime, then the sum of the divisors of n is equal to

    A) n

    B) 2n

    C) pn

    D) \[{{p}^{n}}\]

    Correct Answer: B

    Solution :

    [b] If \[N={{p}_{1}}^{{{\alpha }_{1}}}{{P}_{2}}^{{{\alpha }_{2}}}\] than the sum of the divisors of N is \[\left( \frac{{{p}_{1}}^{{{\alpha }_{1}}+1}-1}{{{p}_{1}}-1} \right)\left( \frac{{{p}_{2}}^{{{\alpha }_{2}}+1}-1}{{{p}_{2}}-1} \right)\]

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