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Prove for every integer n that there exist two integers a and b of opposite parity such

Chapter 3, Problem 38

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QUESTION:

Prove for every integer n that there exist two integers a and b of opposite parity such that an + b is an odd integer.

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QUESTION:

Prove for every integer n that there exist two integers a and b of opposite parity such that an + b is an odd integer.

ANSWER:

Problem 38

Prove for every integer that there exist two integers  and  of opposite parity such that  is an odd integer.

                                                              Step by Step Solution

Step 1 of 3

If two integers have opposite parity, then one is even and the other is odd.

Suppose,is even integer and is an odd integer.

Then by definition of even and odd integers:

 

Here,

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