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

by dimension10
Tags: brocard, existence, paradox
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dimension10
#1
Jul6-11, 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.
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File Type: pdf the nonexistence of {4, 5, 7}.pdf (176.5 KB, 69 views)
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atomthick
#2
Jul6-11, 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]
dimension10
#3
Jul12-11, 03:16 AM
P: 371
Using Euler's reflection formula its correct.

atomthick
#4
Jul12-11, 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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