Question

Find the integer a such that , a\equiv 24 (\bmod 31)\ and\ -15\leq a\leq 15

Analyzing functions
ANSWERED
asked 2021-09-05
Find the integer a such that
\(\displaystyle{a}\equiv{24}{\left({b}\text{mod}{31}\right)}\ {\quad\text{and}\quad}\ -{15}\leq{a}\leq{15}\)

Expert Answers (1)

2021-09-06
\(\displaystyle{a}\equiv{24}{\left({b}\text{mod}{31}\right)}\) We can find a such that \(\displaystyle-{15}\leq{a}\leq{15}\) by consecutively substracting 31 from 24 until we obtain a value between -15 and 15. \(\displaystyle{a}\equiv{24}{\left({b}\text{mod}{31}\right)}\)
\(\displaystyle\equiv{24}-{31}{\left({b}\text{mod}{31}\right)}\)
\(\displaystyle\equiv-{7}{\left({b}\text{mod}{31}\right)}\) SInce -7 is between -15 and 15: \(\displaystyle{a}=-{7}\)
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