Question 134
A piecewise linear periodic function is defined by
$$
f(x) = \begin{cases} x & \text{if } x \in [-1, 1), \\ 2-x & \text{if } x \in [1, 3), \end{cases}
$$
and $f(x+4) = f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern depicted below.
The parabola $x = 34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\frac{a+b\sqrt{c}}{d}$, where $a, b, c$, and $d$ are positive integers, $a, b$, and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.
$$
f(x) = \begin{cases} x & \text{if } x \in [-1, 1), \\ 2-x & \text{if } x \in [1, 3), \end{cases}
$$
and $f(x+4) = f(x)$ for all real numbers $x$. The graph of $f(x)$ has the sawtooth pattern depicted below.
The parabola $x = 34y^2$ intersects the graph of $f(x)$ at finitely many points. The sum of the $y$-coordinates of these intersection points can be expressed in the form $\frac{a+b\sqrt{c}}{d}$, where $a, b, c$, and $d$ are positive integers, $a, b$, and $d$ have greatest common divisor equal to 1, and $c$ is not divisible by the square of any prime. Find $a+b+c+d$.