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

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