Prove or disprove 6 2 mod 4SolutionIf a is not a multiple o

Prove or disprove: -6 = 2 mod 4

Solution

If a is not a multiple of 3, either one of these must hold:

a?1(mod3)

or a?2(mod3)

Basically, those are saying that the remainder on dividing a by 3 is either 1 or 2.

Now, the second can also be expressed as a??1(mod3)

So everything can be more concisely expressed as a?