a) Explanation The integer factors of 500 is 2 2 ⋅ 5 3 . Let A k be the set of positive integers less than or equal to 500 which are divisible by k . The positive integers which are relatively prime to 500 and less than or equal to are those which are not divisible by 2 or 5. 500 − | A 2 ∪ A 5 | = 500 − | A 2 | − | A 5 | + | A 2 ∩ A 5 | | A 2 | = 500 2 = 250 | A 5 | = 500 5 = 100 | A 2 ∩ A 5 | = 500 2 ⋅ 5 = 500 10 = 50 500 − | A 2 ∪ A 5 | = 500 − b) To determine The number ofintegers that are less than 9975 and are relatively prime to 9975.

3rd Edition

ISBN: 9780131679955

Author: Edgar G. Goodaire

Publisher: Prentice Hall

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Chapter 6.1, Problem 12E

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The number ofintegers that are less than 500 and are relatively prime to 500.

To determine

The number ofintegers that are less than 9975 and are relatively prime to 9975.

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Chapter 6.1, Problem 11E

Chapter 6.1, Problem 13E

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The number ofintegers that are less than 500 and are relatively prime to 500.

Solution Summary: The author explains that the number of integers that are less than 500 and are relatively prime to 500 is 200.

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The number ofintegers that are less than 500 and are relatively prime to 500.

The number ofintegers that are less than 9975 and are relatively prime to 9975.

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