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

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.
-$$\text { If } a \equiv b ( \bmod m ) , \text { then } 2 a \equiv 2 b ( \bmod 2 m )$$

Quizplus · Accepted Answer

If $a \equiv b \pmod{m}$, it means $m | (a - b)$. Multiplying both sides of the equation by 2 gives $2m | 2(a - b)$, which implies $2a \equiv 2b \pmod{2m}$.

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