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It says to solve the recurrence exactly for n a power of 2.

T(n) = {1}, if n = 1

T(n) = {5T(n/2) + (n lg n)^2, otherwise

I'm supposed to use Θ notation to express my answer.

Normally I would try to look for the characteristic equation but for this one I'm lost.

Is this the first step?

T(n) - 5T(n/2) = (n lg n )^2

This is not a duplicate as it has not been posted there.

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