Solution: We have **120 = 3 * 5 * 8**

therefore to show that given expression is divisible by 120 ; it is sufficient to show that 3, 5 and 8 are the factors of n^5-5n^3+4n

let us factorise the given expression:

since (n-2), (n-1), n, (n+1) are 4 consecutive integers.

one of it must be divisible by 4.

and at least two out of 5 consecutive integers must be even.

thus it must be divisible by 8.

now again out of three consecutive integers 1 must be divisible by 3.

and out of 5 consecutive integers 1 must be divisible by 5.

thus the given expression is divisible by 3, 5 and 8

**thus it is divisible by 120.**