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Math Help - Standardized Test Question

  1. #1
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    Standardized Test Question

    What is the most efficient approach to this question?
    I am assuming there is some geometric series shortcut which would give me a shortcut. Or is it just a matter of looking at the properties of the final number without actually taking the time to figure it out.

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  2. #2
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
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    Of course, they don't expect you to calculate that, but take advantage of a cool property of this function.

    As defined h(n)=2*4*6*8*...*2k, where 2k=n

    so h(100)=2*4*6*8*...100
    Factorize
    h(100)=2(1*2*3*4*...*50)
    h(100)=2*50!

    Now h(100) is divisible by all the primes below 50, but when we add 1
    h(100)+1=2*50!+1

    It is no longer divisible by any number below 50.
    Last edited by I-Think; November 11th 2009 at 06:27 AM. Reason: Place math labels
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