a) Explain why it is not possible to divide 17 by 0. b) An integer is divided by

Question

a) Explain why it is not possible to divide 17 by 0.

b) An integer is divided by 6. List all possible values for the remainder.

d) Prove that given any integer n, the integer 2 n can be written 3k or 3k+1 for some integer k.

a) Explain why it is not possible to divide 17 by 0. b) An integer is divided by 6. List all possible values for the remainder. c) Explain how the Division Theorem implies that every integer can be written in the form 4k, 4k + 1, 4k + 2, or 4k + 3, for some k in Z. d) Prove that given any integer n, the integer 2 n can be written 3k or 3k+1 for some integer k.

Explanation / Answer

a) Because you can not get 17 by   multiplying any number with zero

b) Reminder are 1, 2, 3, 4, 5

c)when k=0 --> number are 0, 1, 2, 3

when k=1 --> number are 4, 5, 6, 7

and so on

D) for integer n =1

2n = 2

which can not be written in form of 3k or 3k+1 when k is positive integer

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