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August 31st, 2012, 02:59 AM   #1
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Complex equation

I'm perplexed by the following problem:
"Find the number of solutions for n>2 and nN of the following equation:


So far I have worked out:
Z=0 is always a solution.
I can rewrite the original equation like this:



Furthermore, I can see the following:



so, .

Now, I have to solve .
I have no clue how to go about, so any help would be greatly appreciated.
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August 31st, 2012, 03:35 AM   #2
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Re: Complex equation



Implies and for k = 0,1,2,...,n

for k = 0,1,2,...,n



and we are done.

EDIT : @skipjack : Yes, sorry. I have edited that.
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September 2nd, 2012, 01:13 AM   #3
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Dividing 2k? by n gives 2k?/n, not k?/n.
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