“Show that n^4-n^3+n^2-n is divisible by 2 for all positive integers n.”

Kaelithas

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“Show that n^4-n^3+n^2-n is divisible by 2 for all positive integers n.”

Halpppp my crush needs help halp your boii plzz

“Show that n^4-n^3+n^2-n is divisible by 2 for all positive integers n.”
 
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Halpppp my crush needs help halp your boii plzz

“Show that n^4-n^3+n^2-n is divisible by 2 for all positive integers n.”
 
Show that n^4-n^3+n^2-n is divisible by 2 for all positive integers n.

Hint:

Factor out n from the expression. Then factor out (n-1) from the resulting polynomial.

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/for
 
“Show that n^4-n^3+n^2-n is divisible by 2 for all positive integers n.”
Here is a completely different way to attack the problem.

It is given that n is a positive integer. Therefore n is either even or odd. If n is even, all its powers are even, and the sum of any number of even integers is even. How does that help with regard to what you are asked? Now think about the situation if n is odd.

The point is that there may be several ways to think about a problem.
 
still dont get it : (
If one adds four even integers is the sum even?
If one adds four odd integers is the sum even?
If \(\displaystyle j\) is a positive integer & \(\displaystyle n\) is even is \(\displaystyle n^j\) also even?
If \(\displaystyle j\) is a positive integer & \(\displaystyle n\) is odd is \(\displaystyle n^j\) also odd?
 
Halpppp my crush needs help halp your boii plzz

“Show that n^4-n^3+n^2-n is divisible by 2 for all positive integers n.”
Hint:

Factor out n from the expression. Then factor out (n-1) from the resulting polynomial.

Please share your work with us ...even if you know it is wrong.
still dont get it
Since you are not the person working on this exercize, this may be at least part of the issue. So please have your "crush" reply with his/her thoughts and efforts so far, starting with a listing of his/her results from each of the steps provided in the "Hint" instructions. Thank you! ;)
 
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