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For each ordered pair (a, b) of integers define a mapping aa.b : Z -+ Z by aa.b(n) = an

Chapter 1, Problem 1.24

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QUESTION:

For each ordered pair (a, b) of integers define a mapping aa.b : Z -+ Z by aa.b(n) = an + b.(a) For which pairs (a, b) is aa.b onto?(b) For which pairs (a, b) is aa.b one-to-one?

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QUESTION:

For each ordered pair (a, b) of integers define a mapping aa.b : Z -+ Z by aa.b(n) = an + b.(a) For which pairs (a, b) is aa.b onto?(b) For which pairs (a, b) is aa.b one-to-one?

ANSWER:

Step 1 of 3

Following is the mapping

So,

Each ordered pair,  , of integers defines one such mapping.

So, the domain and codomain, both are the set of integers.

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