Let \(\sim_R\) be the relation on \(\mathbb{Z}\) given by \(a \sim_R b\) if and only if there exists \(c \in \mathbb{Z}\) with \(\gcd(c, 17) = 1\) such that \(a \equiv c^2 b \pmod{17}\).(a) Show that \(\sim_R\) is an equivalence relation.(b) Identify the equivalence classes of \(\sim_R\).

A relation which is reflexive symmetric and transitive.

Answered: Let ~R be the relation on Z given by a…

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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Let ~R be the relation on Z given by a ~R b if and only if there exists ce Z with ged(c, 17) = 1 such that a = c²b (mod 17). (a) Show that ~R is an equivalence relation. (b) Identify the equivalence classes of ~R.