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Paradox for the existence of 4,5 and 7 using Brocard's problem 
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#1
Jul611, 08:16 AM

P: 371

I have attatched my Paradox for the existence of 4,5 and 7 using Brocard's problem . I don't know where i have gone wrong as 4,5,7 exist, surely.



#2
Jul611, 09:52 AM

P: 70

On the second page you get [itex]\alpha\cdot sin(\alpha\pi)\Gamma(\alpha) + 1 = x^{2}[/itex] and that is not correct since [itex]sin(\alpha\pi)[/itex] are canceling eachother. The correct result is
[itex]\alpha\Gamma(\alpha) + 1 = x^{2}[/itex] 


#3
Jul1211, 03:16 AM

P: 371

Using Euler's reflection formula its correct.



#4
Jul1211, 03:31 AM

P: 70

Paradox for the existence of 4,5 and 7 using Brocard's problem
Yup, but you apply it twice and therefore the result should have been without the sin(α*pi)



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