Princeton Review, rule 3 :

For any positive integer c, the statement

'a is congruent to b (mod n)'

<=>

'a is congruent to b (mod cn)'

Counter-example :

5 congruent 2 (mod 3)

Let c = 2.

5 congruent 2 (mod 9) is FALSE. Since (5-2) = 3 is not divisible by 9.