For some of the most interesting laws of modular arithmetic (Choose some of your liking, but do include rules (vi) and (vii) ) , write down a similar rule for the MOD n-function and for classes of ZnZn. Theorem [ rules for congruences JLet n be a fixed positive integer, and let a,b, c,d. be any integers.Then the following are true :(i) as a (mod n)(ü) If aib (mod n)then be a Cmod n)(i) IfQ= b Cmod n) and bēc Cmod n) then aE c (mod n)(iv) Ifab (mod n)then a+c= b+c (mod n)(v) IfQ=b (modn) then ac s bc (modn)(vi) IfQ=b (mod n) and c=d cmod n) then a+c Ŝ b+d (mod n)(vii) Ifasb (mod n) and c=d (mod n) then ac = bd (mod n)(vüi) IfQ=b (mod n) then a = b" Cmod n) for anypositive integer k.

This is a problem of mudular arithmatic.

For some of the most interesting laws of modular arithmetic (Choose some of your liking, but do include rules (vi) and (vii) ) , write down a similar rule for the MOD n-function and for classes of ZnZn.

For some of the most interesting laws of modular arithmetic (Choose some of your liking, but do include rules (vi) and (vii) ) , write down a similar rule for the MOD n-function and for classes of ZnZn.

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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