WILL RATE LIFE SAVER!!! IF DETAIL IS SHOWN!!! THANK YOU!!!!! Solution Proof: We

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WILL RATE LIFE SAVER!!! IF DETAIL IS SHOWN!!! THANK YOU!!!!!

Explanation / Answer

Proof: We must first show that and integer d is a common divisor of a and b. Let a and b be integers, not both 0. Let S={n>0|n=ax+by for integers x and y}. Notice that a=a(1)+b(0) and b=a(0)+b(1), so a and b are elements of S. Further, -a=a(-1)+b(0) and -b=a(0)+b(-1), so -a and -b are in S. So S contains at least 1 positive integer. By the Well Ordering Principle, S has a least element, namely d. Since d is in S, there are integers x and y such that d=ax+by. Now, by the Division Algorithm, to divide by d there must be integers q and r such that a=d*q+r where 0

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