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m} be positive integers s orollary 4.3. Let f(x) € Z[x] and {m₁, irwise co-prime and m = m₁m₂ mk. Then f(x) = 0 (m) has a so each of the congruences f(x) = 0 (m₂) has a solution. Moreover, ij enote the number of solutions of f(x) = 0(m) and f(x) = 0(m₁), 1 m) s(m)s(ms)... s(m.) - ...

m} be positive integers s orollary 4.3. Let f(x) € Z[x] and {m₁, irwise co-prime and m = m₁m₂ mk. Then f(x) = 0 (m) has a so each of the congruences f(x) = 0 (m₂) has a solution. Moreover, ij enote the number of solutions of f(x) = 0(m) and f(x) = 0(m₁), 1 m) s(m)s(ms)... s(m.) - ...

Advanced Engineering Mathematics
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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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(m₁) 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).
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(m₁) 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).
let mal be non- ное hove Margolf my Integer and 1(a) be + (P) V Z d[m bag (n)
Transcribed Image Text:let mal be non- ное hove Margolf my Integer and 1(a) be + (P) V Z d[m bag (n)
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