Question 27
The fraction $\frac{1}{2015}$ has a unique "(restricted) partial fraction decomposition" of the form
$$
\frac{1}{2015}=\frac{a}{5}+\frac{b}{13}+\frac{c}{31}
$$
where $a, b, c$ are integers with $0 \leq a \lt 5$ and $0 \leq b \lt 13$. Find $a+b$.
$$
\frac{1}{2015}=\frac{a}{5}+\frac{b}{13}+\frac{c}{31}
$$
where $a, b, c$ are integers with $0 \leq a \lt 5$ and $0 \leq b \lt 13$. Find $a+b$.