Let n1, n2, n3 be three numbers that are pairwise relatively prime so that (n1, n2) = (n2, n3) = (n1, n3). Let a1, a2, and a3 be any integers. We showed in class that the system x ≡ a1 (mod n1) x ≡ a2 (mod n2) x ≡ a3 (mod n3) has a unique solution, say b, modulo n1n2n3. Give a formula for b in terms of a1, a2, a3, n1, n2, and n3. You will need to make use of multiplicative inverses.

Let n1, n2, n3 be three numbers that are pairwise relatively prime so that (n1, n2) = (n2, n3) = (n1, n3). Let a1, a2, and a3 be any integers. We showed in class that the system x ≡ a1 (mod n1) x ≡ a2 (mod n2) x ≡ a3 (mod n3) has a unique solution, say b, modulo n1n2n3. Give a formula for b in terms of a1, a2, a3, n1, n2, and n3. You will need to make use of multiplicative inverses.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.5: Congruence Of Integers

Problem 37E

See similar textbooks