pairwise co-prime and m = m₁m₂ mk. Then f(x) = 0 (m) has a solution if and only if each of the congruences f(x) = 0 (m;) has a solution. Moreover, if s(m) and s(m₁) denote the number of solutions of f(x) = 0(m) and f(x) = 0(m₁), respectively, Then a(m) alm. Valm) alm.)
pairwise co-prime and m = m₁m₂ mk. Then f(x) = 0 (m) has a solution if and only if each of the congruences f(x) = 0 (m;) has a solution. Moreover, if s(m) and s(m₁) denote the number of solutions of f(x) = 0(m) and f(x) = 0(m₁), respectively, Then a(m) alm. Valm) alm.)
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
![Corollary 4.3. Let f(x) = Z[x] and {m₁,...,m} be positive integers such that they are
pairwise co-prime and m = m₁m² mk. Then f(x) = 0 (m) has a solution if and only
if each of the congruences f(x) = 0 (m₂) has a solution. Moreover, if s(m) and s(m₂)
denote the number of solutions of f(x) = 0(m) and f(x) = 0(m₁), respectively, Then
s(m) = s(m₁)s(m₂)... s(mk).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7a5856be-6b27-47ab-a622-536b444de7a5%2F2d312d87-9251-4c0a-aaed-9eba17438d6d%2F6dw86sd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Corollary 4.3. Let f(x) = Z[x] and {m₁,...,m} be positive integers such that they are
pairwise co-prime and m = m₁m² mk. Then f(x) = 0 (m) has a solution if and only
if each of the congruences f(x) = 0 (m₂) has a solution. Moreover, if s(m) and s(m₂)
denote the number of solutions of f(x) = 0(m) and f(x) = 0(m₁), respectively, Then
s(m) = s(m₁)s(m₂)... s(mk).
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