Chapter 4.1A, Problem 9A

Classify each of the following statements as true or false, for all whole numbers a, b, and c, with $b\ne 0$.

a. 7|21 implies $7|{21}^2$.

b. If $b|a$, then $(b+c)|(a+c)$.

c. If $b|a$, then $b^2|a^3$.

d. If $b|a$, then $b|(a+b)$.