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Question Of The Day

    Let N = (1 + 2 + 23 + ….. + 29)(1 + 210 + 220 +…. + 290)(1 + 2100 + 2200 + …. + 2900) + 1. Find how many positive integers other than 1 and N perfectly divides N.  

    a) 0

    b) 99

    c) 1001

    d) 999

     

    Ans: d) 999

     

    N = (1 + 2 + 22 + ….. + 2999) + 1 = (21000 – 1)/(2 – 1) + 1 = 21000

    Total no. of divisors = 1001. Total no. of divisors barring 1 and N = 1001 – 2 = 999

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