Learning Target N1: I can correctly express the congruence relation as a statement of divisibility and vice-versa. I cancompute congruences and perform arithmetic modulo n.1. Compute the following via the division algorithm (i.e. n = dq + r with 0

Let be the remainder when is divided by . then there exists some integer such that , .(a) (b)…

Answered: 1. Compute the following via the…

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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Question

Learning Target N1: I can correctly express the congruence relation as a statement of divisibility and vice-versa. I can
compute congruences and perform arithmetic modulo n.
1. Compute the following via the division algorithm (i.e. n = dq + r with 0 <r <d). Show your work.
(a) 8675 ÷ 309
(b) 555 +213
2. If a = 3 (mod 11) and b = 9 (mod 11), positive and fully-reduced modulo the modulus:
(a) Compute a + b (mod 11)
(b) Compute b2 (mod 11)

Expert Solution

Step 1: Division algorithm:

Let $r$ be the remainder when $n$ is divided by $d$ . then there exists some integer $q$ such that $n equals d q plus r$ , $0 less or equal than r less than d$ .

(a) $8675 divided by 309$

(b) $555 divided by 213$

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