I am having problem of trying to apply the well ordering principle. I know what it is, but i find it difficult to apply it. If anyone knows of any good website that has a lot of useful information, please do let me know. I do not know where to start working on a solution, and i am terribly lost. Below are my questions:
Use the well-ordering principle to prove that if a and b are positive integers, then there exist integers u,v such that gcd(a,b) = ua+vb.
Let a, b be integers, not both zero, and d be a positive integer. Prove that d=gcd(a,b) iff
(i) d|a, d|b and
(ii) for all c element of integers, if c|a and c|b, them c|d.