Post'em.
SQT
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Did I fucked up? Proof of orthogonality of plane waves
Prove that n^5 - 5n^3 + 4n is divisible by 120.
I tried factoring it and I got n(n+1)(n-1)(n+2)(n-2) but I still have no idea why it's divisible by 120. Any help?
how do i implement a hashtable using only arrays?
Put arrays in your array.
n(n+1)(n-1)(n+2)(n-2)
Put it in order:
(n-2)(n-1)n(n+1)(n+2)
Now, it's supposed to be n> 2 otherwise it is impossible.
See that for 3 we have:
(1)(2)3(4)(5) = 6*20 = 120.
For 4 we have:
(2)(3)4(5)(6) = 6*120 = 720
For 5 we have:
(3)(4)5(6)(7). As you can see by now, you'll always have a multiple of 5, 3 and 8(a multiple of 2 and 4 every time). So it'll always divide by 120.
Why is it impossible for n to be 0, 1 or 2? Isn't 0 divisible by 120?
...
> Isn't 0 divisible by 120?
yes it is
If you increase an objects energy, you increase it's gravitational pull. But kinetic energy is just relative, so how does the universe ensure that me moving towards another galaxy wont collapse it? Or is the increase in kinetic energy(and thus gravity) perfectly cancelled with time dialation?
Apologies if i didn't explain correctly, this isn't my field of expertise.