The value of the operation [8][11] in \(\displaystyle{Z}_{{{5}}}\) and to write the answer in the form [r] with \(\displaystyle{0}\leq{r}{<}{m}\).

A Counterexample to the statement, If \(ac\equiv bc\pmod m\), where a,b,c, and m are integers with \(\displaystyle{m}\geq{2}\), then \(a\equiv b \pmod m\).

The value of the expression [9]+[11] in \(\displaystyle{Z}_{{{15}}}\) and to write the answer in the form [r] with \(\displaystyle{0}\leq{r}{<}{m}\).

Solve the following congruence. \(\displaystyle{x}^{{{2}}}\equiv{7}{b}\text{mod}{29}\)

The value of the operation [16]+[9] in \(\displaystyle{Z}_{{{6}}}\) and to write the answer in the form [r] with \(\displaystyle{0}\leq{r}{<}{m}\).