Divisibility: Show that 360 divides s^2 (s^2 - 1) (s^2 - 4).

auliaulfitrah

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I got this question from 'Number Theory' actually, but i dunno where to post it. So, the problem goes like this:

Show that 360 divides s2 (s2 - 1) (s2 - 4).
 
Problems on Divisibility

I encountered this question in 'Number Theory' course. It goes as follows:

Show that 360 divides (no remainder) s^2 (s^2 - 1)(s^2 - 4)
 
I got this question from 'Number Theory' actually, but i dunno where to post it. So, the problem goes like this:

Show that 360 divides s2 (s2 - 1) (s2 - 4).
As posted the problem does not make sense to me.

Please check and confirm its completeness and correctness.
 
As posted the problem does not make sense to me.

Please check and confirm its completeness and correctness.

For s an integer, show that 360 divides \(\displaystyle \ s^2(s^2 - 1)(s^2 - 4)\).

Or:

For s an integer, show that \(\displaystyle \ s^2(s^2 - 1)(s^2 - 4) \ \) is divisible by 360.



Show that 360 divides (no remainder) s^2 (s^2 - 1)(s^2 - 4)

Writing "no remainder" is redundant. Stating that it divides means that there is no remainder.
 
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I encountered this question in 'Number Theory' course. It goes as follows:

Show that 360 divides (no remainder) s^2 (s^2 - 1)(s^2 - 4)
So what have you tried? Did you factor? Do you know the factors of 360? You want help, which is good, but you fail to state what you are having trouble with. The title of the website is free math help, not we will do your homework for you. Please reply back with what you tried.
 
I got this question from 'Number Theory' actually, but i dunno where to post it. So, the problem goes like this:

Show that 360 divides s2 (s2 - 1) (s2 - 4).
Hint:

\(\displaystyle x = s^2(s^2 - 1)(s^2 - 4) = s^2(s - 1)(s + 1)(s - 2)(s + 2) = (s - 2)(s - 1)(s^2)(s + 1)(s + 2).\)

\(\displaystyle \text {Let: } t = s - 2 \implies\)

\(\displaystyle x = t(t + 1)(t + 2)^2(t + 3)(t + 4).\)

Now what?
 
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For s an integer, show that 360 divides \(\displaystyle \ s^2(s^2 - 1)(s^2 - 4)\).

Or:

For s an integer, show that \(\displaystyle \ s^2(s^2 - 1)(s^2 - 4) \ \) is divisible by 360.




Writing "no remainder" is redundant. Stating that it divides means that there is no remainder.
Thank you LA - I had inferred as much.

However, I would have liked the OP to clarify the problem - just see the depth of interest present in "actual solution" of the problem.
 
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