Chapter 8.4, Problem 3ES

To determine

(a)

To verify that $3|(25-19)$.

To determine

(b)

To explain the reason for $25\cong 19(\mathrm{mod}3)$.

To determine

(c)

The value of $k$ for which $25=19+3k$ is true.

To determine

(d)

To find the nonnegative remainder when $25$ is divided by $3$ and also $19$ is divided by $3$.

To determine

(e)

To explain why $25\mathrm{mod}3=19\mathrm{mod}3$.