Chapter 4.5, Problem 17E

(a)

To determine

To prove: That for the test $\text{w}\text{.}\text{a}\equiv 0\left(\mathrm{mod}n\right)$ to be sensible we should have $n>9$.

(b)

To determine

To prove: That the test $\text{w}\text{.}\text{a}\equiv 0\left(\mathrm{mod}n\right)$ will detect single digit errors when $w_i$ is relatively prime to $n$ for all $i$ and $n>9$.

(c)

To determine

To prove: That the test $\text{w}\text{.}\text{a}\equiv 0\left(\mathrm{mod}n\right)$ will detect the error resulting from transposition of $a_i$ and $a_j$ when $w_i-w_j$ is relatively prime to $n$ and $n>9$.