Problem 2. Let p be an odd (rational) prime and Sp be a primitive pth root of unity. Define Ap1- Sp. Prove that the ideal pO(S») factors aspOg(6,) = (AP-1).Hint: Lemma 6 of the course notes together with the geometric series formula shouldprovide one containment. Taking norms should give equality.

proof ; this uses the irreducibility of ϕpx in ℚx. Thus for all a∈ℤ/p×the power is ζa another root…

Problem 2. Let p be an odd (rational) prime and Sp be a primitive pth root of unity. Define dp 1- Sp. Prove that the ideal pOqQ(s») factors as pOQ(s») = (AP-1). %3D Hint: Lemma 6 of the course notes together with the geometric series formula should provide one containment. Taking norms should give equality.

Problem 2. Let p be an odd (rational) prime and Sp be a primitive pth root of unity. Define dp 1- Sp. Prove that the ideal pOqQ(s») factors as pOQ(s») = (AP-1). %3D Hint: Lemma 6 of the course notes together with the geometric series formula should provide one containment. Taking norms should give equality.

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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