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.
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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Question
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.
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