For each k ≥ 1, there exists N such that for every prime p > N, the modular equation xk + yk ≡ zk (mod p) has nonzero solutions x,y,z. For the proof of Schur’s theorem, we will make use of the following fact which says that the multiplicative group of Z/pZ is cyclic. Fact For every prime p, there exists 1 ≤ a ≤ p −1 such that in Z/pZ,
For each k ≥ 1, there exists N such that for every prime p > N, the modular equation xk + yk ≡ zk (mod p) has nonzero solutions x,y,z. For the proof of Schur’s theorem, we will make use of the following fact which says that the multiplicative group of Z/pZ is cyclic. Fact For every prime p, there exists 1 ≤ a ≤ p −1 such that in Z/pZ,
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
For each k ≥ 1, there exists N such that for every prime p > N, the modular equation xk + yk ≡ zk (mod p) has nonzero solutions x,y,z. For the proof of Schur’s theorem, we will make use of the following fact which says that the multiplicative group of Z/pZ is cyclic. Fact For every prime p, there exists 1 ≤ a ≤ p −1 such that in Z/pZ,
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,