determine whether each of the following "theorems" is true or false. Assume that a, b, c, d,
and m are integers with m 1.
-$$\text { If } a \equiv b ( \bmod m ) , \text { then } 2 a \equiv 2 b ( \bmod m )$$

Question

determine whether each of the following "theorems" is true or false. Assume that a, b, c, d,
and m are integers with m > 1.
-$$\text { If } a \equiv b ( \bmod m ) , \text { then } 2 a \equiv 2 b ( \bmod m )$$

Quizplus · Accepted Answer

Multiplying both sides of the congruence $a \equiv b \pmod{m}$ by 2 does not change the truth of the statement, as if $a - b$ is divisible by $m$, then $2(a - b) = 2a - 2b$ is also divisible by $m$, meaning $2a \equiv 2b \pmod{m}$.

Determine Whether Each of the Following "Theorems" Is True or False