Def: An interger "m" divides an integer "n" if there is an integer "q" such that n=mq.

Question

?Suppose a, b, and c are integers such that a divides b and b divides c. Prove that a divides c.

Answer 1

If b is an integer factor of b, and b is an integer factor of x, then

b = ma and c = nb, where m and n are both integers.

It follows that c = m n a. Since m and n are both integers, so is mn. Therefore a is an integer factor of c, or, in other words, "a divides c".