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wythagoras
wythagoras
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edit approved Feb 26, 2016 at 10:20
user268307
edit approved Feb 26, 2016 at 10:20
user268307

proof Prove that 8640$8640$ divides $n^9 - 6n^7 + 9n^5 - 4n^3$.

I found this problem in a book, I can't solve it unfortunately. ProofProve that for all integer values $n$, $n^9 - 6n^7 + 9n^5 - 4n^3$ is divisible by 8640.$8640.$ So far I've noticed that 8460 = 6! * 12$8460 = 6! \times 12$, also I've tried to simplify that expression and I've found that it's equal to this $n^3(n^3-3n-2)(n^3-3n+2)$, but I can't move on after that.

proof that 8640 divides $n^9 - 6n^7 + 9n^5 - 4n^3$

I found this problem in a book, I can't solve it unfortunately. Proof that for all integer values $n$, $n^9 - 6n^7 + 9n^5 - 4n^3$ is divisible by 8640. So far I've noticed that 8460 = 6! * 12, also I've tried to simplify that expression and I've found that it's equal to this $n^3(n^3-3n-2)(n^3-3n+2)$, but I can't move on after that.

Prove that $8640$ divides $n^9 - 6n^7 + 9n^5 - 4n^3$.

I found this problem in a book, I can't solve it unfortunately. Prove that for all integer values $n$, $n^9 - 6n^7 + 9n^5 - 4n^3$ is divisible by $8640.$ So far I've noticed that $8460 = 6! \times 12$, also I've tried to simplify that expression and I've found that it's equal to this $n^3(n^3-3n-2)(n^3-3n+2)$, but I can't move on after that.

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Kareem
Kareem
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proof that 8640 divides $n^9 - 6n^7 + 9n^5 - 4n^3$

I found this problem in a book, I can't solve it unfortunately. Proof that for all integer values $n$, $n^9 - 6n^7 + 9n^5 - 4n^3$ is divisible by 8640. So far I've noticed that 8460 = 6! * 12, also I've tried to simplify that expression and I've found that it's equal to this $n^3(n^3-3n-2)(n^3-3n+2)$, but I can't move on after that.