Exercise 5.4.8. Given (, m,p E Z and a = mod(,n),b = mod(m, n), and c= mod(p,n). Show the following equivalences using Proposition 54.4. %3D (a) mod( + m) + p,n) = (a &b) @c ("Hint) (b) mod(+ (m +p),n) = a (b@c). (c) mod(l-m) -p.n) = (a ob) oc. (d) mod(( -m) + p, n) = (a ©b)@c. %3D
Exercise 5.4.8. Given (, m,p E Z and a = mod(,n),b = mod(m, n), and c= mod(p,n). Show the following equivalences using Proposition 54.4. %3D (a) mod( + m) + p,n) = (a &b) @c ("Hint) (b) mod(+ (m +p),n) = a (b@c). (c) mod(l-m) -p.n) = (a ob) oc. (d) mod(( -m) + p, n) = (a ©b)@c. %3D
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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Please solve only d part within 10 minutes then I will give you double thumps up
Transcribed Image Text:Proposition 5.4.4. Given l, m E Z.
(a) mod(l+m,n) = mod(l, n) mod(m,n),
%3D
(b) mod(l - m,n) = mod(l, n) © mod(m, n).
Exercise 5.4.8. Given (, m,p E Z and a = mod(,n), b= mod(m,n), and
c= mod(p,n). Show the following equivalences using Proposition 5.4.4.
%3D
!!
(a) mod(l +m) + p, n) = (a ☺b)ec. ("Hint*)
%3D
(b) mod(+ (m +p),n) = a (b@c).
(c) mod( -m) -p,n) = (a © b) oc.
(d) mod(l-m) + p.n) = (a ©b)@c.
(e) mod( + m) - ,n) = (a @ b) oc.
Please do part a and d please show step by
step and the hint for part a says that you
will need to use Proposition 5.4.4 twice.
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