MATH135 Lecture Notes - Lecture 7: Prime Number, Coprime Integers, Division Algorithm

• School: University of Waterloo
• Department: Mathematics
• Course: MATH135
• Professor: Gabrielde Morais Coutinho

Document Summary

University of waterloo - fall 2014 - math 135. We will introduce now a very important tool to study properties of divisibility among numbers. Given integers a, b and m (cid:54)= 0, we say that a is congruent to b modulo m if m | (a b). We denote this by a b (mod m). Decide whether or not the two given integers are congruent modulo 4. a = 2, = 6. a = 1, b = 13. a = 4, b = 12. a = 5, b = 21. a = 0, b = 7. Show that m | a if and only if a 0 (mod m). Find an integer m such that 17 and b = 29 are congruent modulo m. find three integers which are pairwise congruent modulo 7. Find ve integers which are pairwise not congruent modulo 5. Find an integer m (cid:54)= 1 such that 15 57 (mod m) and 20 104 (mod m).