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The representation p#+1=m^2 has no solutions for p>2.
http://forum.math.uoa.gr/viewtopic.php?f=39&t=11700
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Συγγραφέας:  dimitrisstah [ 25 Ιουν 2012, 15:45 ]
Θέμα δημοσίευσης:  The representation p#+1=m^2 has no solutions for p>2.

Theorem

The representation p#+1=m^2 has no solutions for p>2.

Proof:

We have:
p#+1=m^2<=>p#=(m+1)(m-1)
By Euclid lemma 2 must divide (m+1) or (m-1) so we have:
p#=2k(2k+2)=4k(k+1)
So p# has as factor 4. We have a contradiction because 2 is the only even factor of p#.

;)

challenge: prove it for n!+1=m^2 and n>7 is an open problem!

Συγγραφέας:  dimitrisstah [ 25 Ιουν 2012, 17:07 ]
Θέμα δημοσίευσης:  Re: The representation p#+1=m^2 has no solutions for p>2.

integer solutions....

http://en.wikipedia.org/wiki/Brocard%27s_problem

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