Hi !! I tried to find information and examples to solve this modulo arithematic problem but couldn't find it.. This is my preparation questions for exam and not assignment.Could someone explain the steps to solve this problem? And, any resource with related examples like this? cheers!!
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$\begingroup$(1) Just do normally and perform modulo at last: $12+22=34\equiv4\pmod{15}$.
(2) Note that $13\equiv -2\pmod{15}$ so $13^{-1}\equiv-8\equiv7\pmod{15}$. Then do normally: $(-12)\times(-8)=96\equiv6\pmod{15}$
(3) Since $5\cdot n\not\equiv1\pmod{15}$ as $5n-1$ cannot be a multiple of $5$, $5^{-1}$ does not exist and hence $\div$ is not well-defined.
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