The product of three consecutive positive int | vedclass

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Question

(A) Let the three consecutive positive integers be $n, (n+1)$,and $(n+2)$.In any set of three consecutive integers,at least one must be even (divisibl

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True

Vedclass · Answer

(A) Let the three consecutive positive integers be $n, (n+1)$,and $(n+2)$.In any set of three consecutive integers,at least one must be even (divisible by $2$) and exactly one must be a multiple of $3$.Since the product contains at least one factor of $2$ and at least one factor of $3$,the product must be divisible by $2 	imes 3 = 6$.For example,if $n=1$,the product is $1 	imes 2 	imes 3 = 6$,which is divisible by $6$.If $n=2$,the product is $2 	imes 3 	imes 4 = 24$,which is divisible by $6$.Thus,the statement is true.

The product of three consecutive positive integers is always divisible by $6$.

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