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Prove that if n is an integer, then 3n + 1 and 5n + 2 are of opposite parity

Chapter 3, Problem 4

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QUESTION:

Prove that if n is an integer, then 3n + 1 and 5n + 2 are of opposite parity.

Questions & Answers

QUESTION:

Prove that if n is an integer, then 3n + 1 and 5n + 2 are of opposite parity.

ANSWER:

Problem 4

Prove that if  is an integer, then  and  are of opposite parity.

Step by step solution

Step 1 of 4

Consider the following corresponding to some integer ‘k’,

     - A number of the form  is always an even number.

     - A number of the form  is always an odd number

To Prove: The terms  and  are of opposite parity.

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