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.
Here's a little comparison of regular and strong induction that might help you understand it better:
Strong induction versus weak induction
And here's a link that might help clarify the well-ordering principle: Well Ordering Principle
Hope it helps.
Thanks for the links, based on my understand strong mathematical induction requires the step of proving by introducing another variable. So instead of one variable b, we have another additional variable a. So if "a value"<=a<b, so if all values of a is true, then b will also be true considering that b>a right? Hope that makes some sense ...