What's the proof for (2n ± 1)² - 1 = 8x (ie an odd number squared, minus one, equals a multiple of 8)?
I've played around a bit and factorised it down to 4n(n-1) or something similar to that, and also looked at the pattern between the variables n and x that i used in my question. I only know up to year 11 maths, is that enough to proove it?
Update:oh yay thanks, I've done it dozens of times and always had to stop there. haha now I wish I'd figured it out myself
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Continuing from where you stopped:
If n is even i.e. n=2k, then n-1=2k-1 and 4n(n-1) = 8k(2k-1) = 8x.
If n is odd i.e. n=2k+1, then n-1=2k and 4n(n-1)=4(2k+1)2k=8x.
Um mmmmm...
I have cheese in my fridge...three different types of cheese...one of them is a goat cheese.
This is far to complicated for me. I hate complex problems....
But I like cheese...and if you like cheese you are welcome to come around and have some cheese at my house.
Bring crackers.