Show that product of any three consecutive integers is divisible by 3 factorial
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If n=3p+2, then n+1=3p+2+1=3p+3=3(p+1) is divisible by 3. So, we can say that one of the numbers among n,n+1 and n+2 is always divisible by 3 that is: n(n+1)(n+2) is divisible by 3. Similarly, whenever a number is divided by 2, the remainder obtained is either 0 or 1.
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