Question

# Find the integer a such that, a\equiv -15 (\bmod 27)\ and\ -26\leq a\leq 0

Analyzing functions
Find the integer a such that
$$\displaystyle{a}\equiv-{15}{\left({b}\text{mod}{27}\right)}\ {\quad\text{and}\quad}\ -{26}\leq{a}\leq{0}$$

Division algorithm Let a be an integer and d a positive integer. Then there are unique q and r with 0$$\displaystyle{q}={a}\div{d}$$
$$\displaystyle{r}={a}{b}\text{mod}{d}$$
$$\displaystyle{a}\equiv-{15}{\left({b}\text{mod}{27}\right)}\ {\quad\text{and}\quad}\ -{26}\leq{a}\leq{0}$$ Since -15 is between -26 and 0: $$\displaystyle{a}=-{15}$$