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If d | n, then n is a multiple of d, and n is in S.
for the 2nd part, I see that d | n but I don't see how d | n can show that S is all the integer multiples of d
Thanks! The book is called "Introduction to Abstract Mathematics", the class is titled "Intro to logic for secondary mathematics". Thanks for all your help.. i took this class as an elective thinking it would be easier than most of the other upper level math classes, but its turned into a real pain in the math.
For the second one, you use the fact that if d = gcd(a, b) and n = ax + by for some n in Z, then d | n. It should be straightforward from there.
To prove it's unique, let d = gcd(a, b), and then assume there is another gcd, e. It should be fairly easy from here, because one property of the gcd is that it is the greatest common divisor of a and b. Can you have two greatests?
Given this theorem: