An expression like
x=1+\frac{1}{2+\frac{1}{3+\frac{1}{4}}}
is called a continued fraction.
(a) Write x given above as a reduced fraction of the form \frac{a}{b} where a and b are positive integers.
(b) Write \frac{355}{113} as a continued fraction in the form a+\frac{1}{b+\frac{1}{c}}, where a, b, c are positive integers.
(c) Let
y=8+\frac{1}{8+\frac{1}{8+\frac{1}{8+\cdots}}}
where the process continues indefinitely. Given that y can be written in the form p+\sqrt{q}, find the integers p and q.