# Show that the product of three consecutive positive integers is always divisible by 6.

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(proof by contradiction)

Suppose there exists a product of 3 consecutive positive integers that is not divisible by**6** :

Repeating the whole argument we see that

This is a contradiction because and .The only resolution to this contradiction is that there doesn't exist a product of**3** consecutive positive integers not divisible by **6**. That is, the product of any **3** consecutive positive integers is divisible by **6**.

Suppose there exists a product of 3 consecutive positive integers that is not divisible by

Repeating the whole argument we see that

This is a contradiction because and .The only resolution to this contradiction is that there doesn't exist a product of