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

**Question description**

The question is: find the gcd of 2^{21} - 1 and 2^{10} + 1.

The answer is 1.

I started off with: (2^{21} - 1) = (2^{10} + 1)*2^{11} - 2^{11} - 1

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

(2^{10} + 1) = (-2^{11} - 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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