Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
pairwise co-prime and m = mymy m. Then f(1) = 0 (m) has a soluti if each of the congruences f(x) = 0 (m) has a solution. Moreover, if s denote the number of solutions of f(x) = 0(m) and f(x) = 0(m.), resp x(m) x/mx/m slm

pairwise co-prime and m = mymy m. Then f(1) = 0 (m) has a soluti if each of the congruences f(x) = 0 (m) has a solution. Moreover, if s denote the number of solutions of f(x) = 0(m) and f(x) = 0(m.), resp x(m) x/mx/m slm

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
See similar textbooks
icon
Related questions
Question

prove the corolary

Corollary 4.3. Let f(x) € Zr] and {mma} be positive integers such that they are pairwise co-prime and m = mmm. Then f(1) = 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(m.) denote the number of solutions of f(x) = 0(m) and f(x) = 0(m.), respectively. Then s(m) = s(m₁)s(m₂)...s(m.).
Transcribed Image Text:Corollary 4.3. Let f(x) € Zr] and {mma} be positive integers such that they are pairwise co-prime and m = mmm. Then f(1) = 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(m.) denote the number of solutions of f(x) = 0(m) and f(x) = 0(m.), respectively. Then s(m) = s(m₁)s(m₂)...s(m.).
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS