Intermediate Micro-economics/Calculus Question

[Keno]

OK BG, help me out in my most desperate times. Heres my problem: I'm working with a Cournot oligopoly and profit maximization. I understand everything perfectly when dealing with firms of same costs and no fixed costs. And as you know, in a Cournot oligopoly with no fixed costs there can be an infinite number of firms in the market; however when fixed costs are introduced into the cost equation then firms will only enter the market so long as profit is > 0. So I need to figure out in general terms how many firms, N, will enter a given market given these parameters:

P=a+Q (Price equals demand plus total supply)
Q=q1+q2+q3+...+qn-1+qn (total supply equals the sum of all individual firms supply)
qi=(a-c-t)/(1+n) (the quantity that any firm will produce is equal to [the demand minus the marginal cost minus the tax] divided by [1 + the total amount of firms in the market])
TC=cq + f + tq (total cost is equal to the marginal cost multiplied by the amount produced of any firm plus its fixed costs plus the tax multiplied by the amount any firm produces)
Profit=Revenue-Costs=Pq - TC (profit is equal to price multiplied by quanity produced by one firm minus the total costs)

Anyone that can help me will probably know this, but just to refresh you: in a Cournot oligopoly all firms are identical in nature. Also assume that all firms are price takers and that they have equal TC functions.

So I know how many firms will enter the market when fixed costs are present is (a-c)/(f-1)^(1/2), but I don't know how to derive it, which is what I need to do. Please halp!

[Snowknight26]

in a Cournot oligopoly all firms are identical in nature

Isn't that a pure competition market?

[Keno]

It is only if there are no fixed costs, then yes, it will be a pure competition market. When there are fixed costs though then there is a n such that n>n1 will make profit < 0. I think I figured it out though, still working on the proof. Any help would still be greatly appreciate though.

[Keno]

I figured it out finally. I was retarded and set the market profit equals to zero when I needed to set a firm's profit equal to zero. Wow, what a huge waste of time. If anybody wants the entire proof, PM me. Lock and/or let die please.