# Calculating the GCD of 2^21 - 1 and 2^10 + 1

Anonymous

Question description

The question is: find the gcd of 221 - 1 and 210 + 1.

I started off with: (221 - 1) = (210 + 1)*211 - 211 - 1

And then kept applying the Euclidean algorithm e.g. the next line being:

(210 + 1) = (-211 - 1)*(-2-1) - 2-1 + 1

But I'm 8 lines in and it seems like it could go on forever. Can anybody help me out?

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