Corollary 4.3. Let f(x) = Z[x] and {m₁,...,m} be positive integers such that they arepairwise co-prime and m = m₁m² mk. Then f(x) = 0 (m) has a solution if and onlyif 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, Thens(m) = s(m₁)s(m₂)... s(mk).

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Answered: pairwise co-prime and m = m₁m₂ mk. Then…

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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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.)