Question

Find the largest integer S which is a divisor of

Answer 1

\[\huge \color{crimson}{n^5-17n^3+16n}\] for all integer \[\huge \color{crimson}{n \ge4}\]

Answer 2

so far what i did\[n^5-17n^3+17n-n=n(n^4-1)-17n(n^2-1)=(n^2-1)^2(n^3+n-17)\]

Answer 3

You can find the greatest common divisor of two numbers using the Euclidean Algorithm.

You are asked to find an integer S that divides all the terms of the sequence.

i am not sure bout this

Answer 4

I was unable to crack this one.

Answer 5

wat pre-knowledge in number theory shud i have for this one
divisibility or Euclid Algorithm or basic equation properties

Answer 6

n^5 -17n^3 + 16n
n(n^4 - 16n^2 -n^2+ 16)
n(n^2 - 1)(n^2 -16)
n(n-1)(n+1)(n-4)(n+4)

Answer 7

We need to find its HCF, is that right ?

Answer 8

I am not sure if I am following ?

Answer 9

@mukushla