1. ## 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

2. Actually I figured it out
It's 12 .
I worked backwords..

3. Originally Posted by foreverbrokenpromises
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