MATH135 Study Guide - Rational Root Theorem

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: Mike Eden

Document Summary

Since a | b, by definition of divides, there exists an integer k such that ak = b. Since b | c, by definition of divides, there exists an integer h such that bh = c. Substitute ak into b and akh = c. Since kh is an integer, it follows that a | c: divisibility of integer combinations (dic) If a | b and a | c, then a | (bx + cy) for any x, y . Since a | b, there exists an integer k such that ak =b. Since a | c, there exists an integer h such that ah = c. Substitute b and c for ak and ah bx + cy = akx + ahy = a(kx + hy) since kx + hy is an integer it follows that a | (bx + cy) since a(kx + hy) If a | b and b 0 then | a | | b|