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Suppose that integers c, d such that and are positive integers such that b2 – 2a? = 1. Prove that there exist positive are consecutive terms in some Farey sequence and а, a V2 d' (Hint: guess expressions for C, d in terms of a, b that seem to work, then prove that they do.)

Suppose that integers c, d such that and are positive integers such that b2 – 2a? = 1. Prove that there exist positive are consecutive terms in some Farey sequence and а, a V2 d' (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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Suppose that a, b are positive integers such that b2 – 2a? = 1. Prove that there exist positive integers c, d such that and ; are consecutive terms in some Farey sequence and a 1 C V2 d (Hint: guess expressions for C, d in terms of a, b that seem to work, then prove that they do.)
Transcribed Image Text:Suppose that a, b are positive integers such that b2 – 2a? = 1. Prove that there exist positive integers c, d such that and ; are consecutive terms in some Farey sequence and a 1 C V2 d (Hint: guess expressions for C, d in terms of a, b that seem to work, then prove that they do.)
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