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Thread: Functions

  1. #1
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    Functions

    A function $\displaystyle f(n)$, defined for positive integers $\displaystyle n$, always has integer values. The function has the property that $\displaystyle f(kn)$=$\displaystyle k^2f(n) + r$, where $\displaystyle r$ is one of the integers 0, 1, 2, 3.... ($\displaystyle k^2$-1). If $\displaystyle f$(119)= 626, then $\displaystyle f$(17) =

    a) 10 b) 11 c) 12 d) 13 e)14
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  2. #2
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    Actually I figured it out
    It's 12 .
    I worked backwords..
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  3. #3
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    Quote Originally Posted by foreverbrokenpromises View Post
    A function $\displaystyle f(n)$, defined for positive integers $\displaystyle n$, always has integer values. The function has the property that $\displaystyle f(kn)$=$\displaystyle k^2f(n) + r$, where $\displaystyle r$ is one of the integers 0, 1, 2, 3.... ($\displaystyle k^2$-1). If $\displaystyle f$(119)= 626, then $\displaystyle f$(17) =

    a) 10 b) 11 c) 12 d) 13 e)14
    $\displaystyle f(kn)$=$\displaystyle k^2f(n) + r$,
    where $\displaystyle r$ is one of the integers 0, 1, 2, 3.... ($\displaystyle k^2$-1).

    $\displaystyle f$(119)= 626

    119 = 7 x 17

    $\displaystyle f$( 7 $\displaystyle \times $ 17 ) =

    $\displaystyle 7^2 \times $ $\displaystyle f$ (17) + r

    $\displaystyle \frac {626}{49} = 12 $ with remainder of 38

    thus

    Spoiler:

    $\displaystyle f$(17) = c
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