(wa Find the least non-negndive sontion tw the system of congraences wring CR T. X= 3 mod 7 X = 4 mod 11 X = s mod 13

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
icon
Concept explainers
Topic Video
Question

Number Theory

**Problem Statement:**

Find the least non-negative solution to the system of congruences using the Chinese Remainder Theorem (CRT):

\( x \equiv 3 \mod 7 \)

\( x \equiv 4 \mod 11 \)

\( x \equiv 5 \mod 13 \)

**Explanation:**

The Chinese Remainder Theorem (CRT) provides a method to find a unique solution to a system of simultaneous congruences with pairwise coprime moduli. For this problem, we need to solve the given system of congruences to find the smallest non-negative integer \( x \) that satisfies all the congruences simultaneously.
Transcribed Image Text:**Problem Statement:** Find the least non-negative solution to the system of congruences using the Chinese Remainder Theorem (CRT): \( x \equiv 3 \mod 7 \) \( x \equiv 4 \mod 11 \) \( x \equiv 5 \mod 13 \) **Explanation:** The Chinese Remainder Theorem (CRT) provides a method to find a unique solution to a system of simultaneous congruences with pairwise coprime moduli. For this problem, we need to solve the given system of congruences to find the smallest non-negative integer \( x \) that satisfies all the congruences simultaneously.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Application of Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
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,