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2. Let f: Z²Z² be given by f(m, n) = (m-n, n). The composite functions fk, for k € Z+, → are defined as fi(m, n) = f(m,n), and fk+1(m, n) = f(fk(m, n)), for k € Z+. Give a formal proof by induction that fk(m, n) = (m- kn, n), for all k € Zt.

2. Let f: Z²Z² be given by f(m, n) = (m-n, n). The composite functions fk, for k € Z+, → are defined as fi(m, n) = f(m,n), and fk+1(m, n) = f(fk(m, n)), for k € Z+. Give a formal proof by induction that fk(m, n) = (m- kn, n), for all k € Zt.

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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2. Let f: Z²Z² be given by f(m, n) = (m-n, n). The composite functions fk, for k € Z+, are defined as fi(m, n) = f(m,n), and fk+1(m, n) = f(fk(m, n)), for k € Z+. Give a formal proof by induction that f(m, n) = (m-kn, n), for all k € Zt.
Transcribed Image Text:2. Let f: Z²Z² be given by f(m, n) = (m-n, n). The composite functions fk, for k € Z+, are defined as fi(m, n) = f(m,n), and fk+1(m, n) = f(fk(m, n)), for k € Z+. Give a formal proof by induction that f(m, n) = (m-kn, n), for all k € Zt.
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