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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.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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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(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).
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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