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.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 23E
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