MA101 Lecture Notes - Lecture 2: Surjective Function, Euclidean Algorithm, Diophantine Equation

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25 Sep 2016
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An integer m divides an integer n, and we write m | n, if there exists an integer k so that n = km. Since a | b, there exists an integer r so that ka = b. Since b | c, there exists an integer s so that jb = c. Substituting ka for b in the previous equation, we get c= jka. Since jk is an integer, a | c. If a | b and a | c, then a | (bx + cy) for any x, y. Since a | b, there exists an integer k such that b = ka. Since a | c, there exists an integer l such that c = la. Now bx + cy = kax + lay = a(kx + ly ). Z, it follows that a | (bx + cy). If a | b and b 0 then |a| |b|.

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