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(4) Suppose that a, b are positive integers such that 6² – 2a² = 1. Prove that there exist positive integers c, d such that % and are consecutive terms in some Farey sequence and a 1 C < d' √2 (Hint: guess expressions for c, d in terms of a, b that seem to work, then prove that they do.)

(4) Suppose that a, b are positive integers such that 6² – 2a² = 1. Prove that there exist positive integers c, d such that % and are consecutive terms in some Farey sequence and a 1 C < d' √2 (Hint: guess expressions for c, d in terms of a, b that seem to work, then prove that they do.)

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
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(4) Suppose that a, b are positive integers such that 62 – 2a? = 1. Prove that there exist positive integers c, d such that and are consecutive terms in some Farey sequence and a 1 V2 (Hint: guess expressions for c, d in terms of a, b that seem to work, then prove that they do.) b d'
Transcribed Image Text:(4) Suppose that a, b are positive integers such that 62 – 2a? = 1. Prove that there exist positive integers c, d such that and are consecutive terms in some Farey sequence and a 1 V2 (Hint: guess expressions for c, d in terms of a, b that seem to work, then prove that they do.) b d'
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