(a) Assume that n1, n2 and n3 are integers withged(n1, n2) = gcd(n2, n3) = gcd(n1, n3) = 1. Let aj, a2 and az be integers and letN1 = n2n3, N2 = n,n3 and N3 = n¡n2.Consider the integer z = a,N1) + azNw2) + azN(ns).Prove that r = a1 mod n1, I = a2 mod ng and r = a3 mod n3(b) Use part (a) to find a solution to the system of congruencesI = 3 mod 8, I = 2 mod 3, r = 1 mod 5

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(a) Assume that n1, n2 and n3 are integers with gcd(n1, n2) = gcd(n2, n3) = gcd(n1, n3) = 1. Let a1,az and az be integers and let N1 = nzn3, N2 = n¡n3 and N3 = nịn2. Consider the integer 1= a,N1) + ażNw2) + azN(ma). Prove that r = ɑ1 mod n1, 1 = az mod n2 and z = a3 mod n3 (b) Use part (a) to find a solution to the system of congruences I = 3 mod 8, I = 2 mod 3, r=1 mod 5

(a) Assume that n1, n2 and n3 are integers with gcd(n1, n2) = gcd(n2, n3) = gcd(n1, n3) = 1. Let a1,az and az be integers and let N1 = nzn3, N2 = n¡n3 and N3 = nịn2. Consider the integer 1= a,N1) + ażNw2) + azN(ma). Prove that r = ɑ1 mod n1, 1 = az mod n2 and z = a3 mod n3 (b) Use part (a) to find a solution to the system of congruences I = 3 mod 8, I = 2 mod 3, r=1 mod 5

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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