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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
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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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 J Let 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) If Q= b Cmod n) and bēc Cmod n) then aE c (mod n) (iv) If ab (mod n) then a+c= b+c (mod n) (v) If Q=b (modn) then ac s bc (modn) (vi) If Q=b (mod n) and c=d cmod n) then a+c Ŝ b+d (mod n) (vii) If asb (mod n) and c=d (mod n) then ac = bd (mod n) (vüi) If Q=b (mod n) then a = b" Cmod n) for any positive integer k.
Transcribed Image Text:Theorem [ rules for congruences J Let 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) If Q= b Cmod n) and bēc Cmod n) then aE c (mod n) (iv) If ab (mod n) then a+c= b+c (mod n) (v) If Q=b (modn) then ac s bc (modn) (vi) If Q=b (mod n) and c=d cmod n) then a+c Ŝ b+d (mod n) (vii) If asb (mod n) and c=d (mod n) then ac = bd (mod n) (vüi) If Q=b (mod n) then a = b" Cmod n) for any positive integer k.
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