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

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

Quizplus · Accepted Answer

If $a \equiv b \pmod{m^2}$, it means $m^2$ divides $a - b$. Since $m^2$ divides $a - b$, $m$ also divides $a - b$, hence $a \equiv b \pmod{m}$.

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