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(1) (a) Show that the relation a = b mod n if n | a – b is an equivalence relation (b) Show that the binary operations + is well-defined modulo n.

(1) (a) Show that the relation a = b mod n if n | a – b is an equivalence relation (b) Show that the binary operations + is well-defined modulo n.

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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(1) (a) Show that the relation a = b mod n if n | a - b is an equivalence relation (b) Show that the binary operations + is well-defined modulo n. (2) If a = b mod n and a = b mod m and ged(m, n) = 1, then a = b mod mn. (3) Show that for any n E N, n(n + 1)(2n + 1) k=1 (4) Let p be a prime number. Then r2 = 1 mod p has exactly two solutions modulo p.
Transcribed Image Text:(1) (a) Show that the relation a = b mod n if n | a - b is an equivalence relation (b) Show that the binary operations + is well-defined modulo n. (2) If a = b mod n and a = b mod m and ged(m, n) = 1, then a = b mod mn. (3) Show that for any n E N, n(n + 1)(2n + 1) k=1 (4) Let p be a prime number. Then r2 = 1 mod p has exactly two solutions modulo p.
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