Answered: (a) (Z4, +). (b) (Z5, ). (c) (Z3, +).…

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(a) (Z4, +). (b) (Z5, ). (c) (Z3, +). (d) (Z4, ). (e) (Z3, .).

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter12: Sequences, Series And Binomial Theorem

Section12.4: Binomial Theorem

Problem 12.78TI: Find the coefficient of the x4 term of (x+2)7.

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Question

In a semigroup (G,°), we define the power as a^n = a°a°...°a (n times) for every element a ∈ G and every natural number n ∈ N. In which of the following semigroups does 2^2005 = 0 hold true?

(a) (Z4, +).
(b) (Z5, ).
(c) (Z3, +).
(d) (Z4, ).
(e) (Z3, .).

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