SOLUTION: if n > 2 ,then show that n^5-5n^3+4n is divisible by 120

Question 745014: if n > 2 ,then show that n^5-5n^3+4n is divisible by 120
Answer by tommyt3rd(5050) (Show Source): You can put this solution on YOUR website!
Clearly we assume that n is an integer...

First let's factor:

next we rearrange them is succession:

which shows that this is a product of 5 consecutive numbers starting with n-2
and

Now notice that if n>2 the each product is
1*2*3*4*5
2*3*4*5*6
3*4*5*6*7
and so on
each of which is a multiple of 3 (every third digit), 5 (every fifth digit), and 8 (there will always be a multiple of 2 and a multiple of 4).
Therefore they will always divide 120.

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