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Math Help - integers and divisibility

  1. #1
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    integers and divisibility

    Find the smallest positive integer n such that 2n −1 is divisible by 47.
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  2. #2
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    Hello, anncar!

    Find the smallest positive integer n such that 2n -1 is divisible by 47.

    If 2n-1 is divisible by 47, then: . 2n-1 \:=\:47a for some integer a.

    . . Then we have: . n \:=\:\frac{47a+1}{2}


    Since n is a positive integer, 47a+1 is divisible by 2.

    . . The least value occurs when a = 1


    Therefore: . n \;=\;\frac{47(1) + 1}{2}\quad\Rightarrow\quad\boxed{n \:=\:24}

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