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Paradox for the existence of 4,5 and 7 using Brocard's problem

  1. Jul 6, 2011 #1
    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.
     

    Attached Files:

  2. jcsd
  3. Jul 6, 2011 #2
    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]
     
  4. Jul 12, 2011 #3
    Using Euler's reflection formula its correct.
     
  5. Jul 12, 2011 #4
    Yup, but you apply it twice and therefore the result should have been without the sin(α*pi)
     
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