Question

Prove that the product of 3 consecutive numbers is divisible by 6

Answer 1

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Let three consecutive positive integers be n, n+1 and n+2

When a number is divided by 3, the remainder obtained is either 0 or 1 or 2 .

Therefore, n=3p or 3p+1 or 3p+2 , where p is some integer.

If n=3p, then n is divisible by 3.

If n= 3p+1,

n+2=3p+1+2=3p+3=3(p+1) is divisible by 3.

If n = 3p+2 , 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.

= n(n+1) (n+2) is divisible by 3.

Similarly, same as ⬆ up. ❤⚡✨

Answer 2

Answer:

hey dear here's your answer ,.,,

n3 − n = (n − 1)n(n + 1)

is the product of three consecutive integers

and

so is divisible by 6.

n5 − n =

n(n2 − 1)(n2 +1)

= (n3 − n)(n2 + 1)

so it is divisible by 6.

hope it's helpful for you.