Compute gcd(2002 + 2, 20022+2, 20023+2, …)
In order to evaluate , we first evaluate . Before we start the Euclidean algorithm, we can simplify this problem considerably by rewriting in terms of
Substituting from , we now need to find
From , we know that is at most . Since , all we need to do is prove or disprove
This is an easy proof to make.
Therefore, all we need to show is that . Notice that so
Therefore, because , then it must be the case that .