An integer satisfies and if and only if .

Look at first. This is a completely unnecessary congruence because regardless of what is this congruence always holds, therefore we can throw it away.

Look at , since you can divide both sides by to get an equivalent congruence .

Look at , since and we replace it by and equivalent congruence after dividing by 2. This can be further simplifed to the congruence .

Look at , since we get .

Therefore, we are left with, . These congruences now get solved with the Chinese remainder theorem, however I liked to do it without the Chinese remainder theorem, so I show you how I do these sort of problems. Notice that is equivlanet to because . Thus, we are left with . Note that so we have . This combines into since .