Though the proofs are clear for the greatest common divisor, it seems as if the same thing was being stated twice when discussing the 2nd definition of greatest common divisor. I don't see what the distinguishing part is about the other definition such that it is worth restating differently since we already proved everything to go into that definition.
I like the Euclidean Algorithm as it is naturally recursive. I decided that I will write a simple program in C++ to solve for the greatest common divisor. I am a little frustrated as I do not yet know the conventions for recursion in C++ but I am sure I'll figure it out.
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