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Discrete Mathematics and its Applications

Kenneth H. Rosen

$Math Studyset Vaia Explanations$ Math

7th Edition · 808 pages

ISBN: 9780073383095

Chapter 4: Q49E (page 273)

Prove that the product of any three consecutive integers is divisible by 6.

Short Answer

Expert verified

The product of any three consecutive integers is divisible by 6.

Step by step solution

Step: 1

Consider the product of any three consecutive integers. Because every second integer is divisible by 2, the product is divisible by 2.

Step: 2

Because every third integer is divisible by 3, the product is divisible by 3. Therefore the product has both 2 and 3 in its prime factorization and is therefore divisible by 3.2=6

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Prove that the product of any three consecutive integers is divisible by 6.

Short Answer

Step by step solution

Step: 1

Step: 2

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