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

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

Quizplus · Accepted Answer

If $a \equiv b \pmod{2m}$, it means $a - b$ is divisible by $2m$. Since $2m$ is a multiple of $m$, $a - b$ is also divisible by $m$, which implies $a \equiv b \pmod{m}$.

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