Question

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

Analyzing functions
ANSWERED
asked 2021-09-13
Find the integer a such that
\(\displaystyle{a}\equiv-{15}{\left({b}\text{mod}{27}\right)}\ {\quad\text{and}\quad}\ -{26}\leq{a}\leq{0}\)

Expert Answers (1)

2021-09-14
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: \(\displaystyle{a}=-{15}\)
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