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

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.
-$$\text { If } a \equiv b ( \bmod m ) \text { and } c \equiv d ( \bmod m ) \text {, then } a c \equiv b + d ( \bmod m )$$

Quizplus · Accepted Answer

The correct property is $ac \equiv bd \pmod{m}$, not $ac \equiv b + d \pmod{m}$. The given statement incorrectly combines the results of modular arithmetic multiplication and addition.

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