What are the elements of each order in D_n+Z_9 for n = 7 and 11?

ccrfan44
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Pick a number n which is the product of 2 distinct primes 5 or more. Find the number of elements of each order in the groupd D(sub)n+Z(sub)9, completely explaining your work. Verify that these number add up to the order of the group.

Ive used 7 and 11 as my primes. So now do I use these primes in D_n since to where i get D_7+Z_9 and D_11+Z_9? This is where I am confused.
 
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Also once i have that info, then where do i go from here?
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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