Can 8n*3-2n divided by6?

Question

Can 8n*3-2n divided by6?

Why

更新:

THANK you

i am form 2 these year and quite good at maths

my principal give our class some question like it and want us to proof them

so

i'm extremly happy to recieved your answer

Answer 1

最佳解答

I persume that n is a positive integer in your expression.

By MI,

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2008-09-04 19:40:08 補充：

But then, your n could be a negative integer as well, so you may verify the result by factorization:

8n^3 - 2n = 2n ( 4n^2 - 1 ) = 2n ( 2n + 1 )( 2n - 1 )

2008-09-04 19:40:12 補充：

For any 3 consecutive integers, at least one of them is a multiple of 2 and one of them must be a multiple of 3, hence 2n ( 2n + 1 )( 2n - 1 ) is divisible by 6, n being an integer.

2008-09-04 20:19:44 補充：

我覺得係三次方, 如果唔係根本就冇得做!

2008-09-08 22:12:59 補充：

So, if you are only Form 2 and have not learnt anything about MI, just look at the method of factorization as shown above.

資料來源： My Maths Knowledge

Answer 2

to發問者:

如果你個*係代表乘,咁第一個ans係岩

如果個*代表次方,咁第二個ans係岩

Answer 3

Let P(n) be the proposition'8n*3-2n' divided by6.

　When n=1

　　　　＝８（１）．３－２（１）

　　　　＝２２

∴(8n*3-2n) can not divided by6.

資料來源： 自己