Discrete Math (a) Solve the congruence relation 3x + 5 ≡ 2(3 − 5x) (mod 35) for x. (b) If a ≡ b (mod n) and c ≡ d (mod n), show that ac ≡ bd (mod n). (c) Z∗ 39, the set of all the reduced residue classes modulo 39. (d) φ(39), where φ is the Euler φ-function.

Discrete Math (a) Solve the congruence relation 3x + 5 ≡ 2(3 − 5x) (mod 35) for x. (b) If a ≡ b (mod n) and c ≡ d (mod n), show that ac ≡ bd (mod n). (c) Z∗ 39, the set of all the reduced residue classes modulo 39. (d) φ(39), where φ is the Euler φ-function.

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

Discrete Math

(a) Solve the congruence relation 3x + 5 ≡ 2(3 − 5x) (mod 35) for x.
(b) If a ≡ b (mod n) and c ≡ d (mod n), show that ac ≡ bd (mod n).
(c) Z∗ 39, the set of all the reduced residue classes modulo 39.
(d) φ(39), where φ is the Euler φ-function.

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