## Interesting page for the number crunchers

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• Namely, when is a repunit a square in a given base: http://www.mathematik.uni-bielefeld.de/~sillke/PROBLEMS/reputnic_squares Jon Perry perry@globalnet.co.uk
Message 1 of 3 , Jun 1, 2002
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Namely, when is a repunit a square in a given base:

http://www.mathematik.uni-bielefeld.de/~sillke/PROBLEMS/reputnic_squares

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com
• Standard Pellian analysis shows that (x^4-1)/(x-1)=y^2 has no integer solution for odd x in [9,10^20000] The probabilty of a solution with odd x 10^20000 is
Message 2 of 3 , Jun 1, 2002
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Standard Pellian analysis shows that
(x^4-1)/(x-1)=y^2
has no integer solution for
odd x in [9,10^20000]

The probabilty of a solution with
odd x > 10^20000 is about
1 part in 10^10000, so
I wouldn't advise "number crunching" :-)

David
• Two points: 1) Does the Mordell conjecture still hold for y^n? 2) I think this is the law of small numbers, but how is the theorem that if an equation has no
Message 3 of 3 , Jun 1, 2002
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Two points:

1) Does the Mordell conjecture still hold for y^n?

2) I think this is the law of small numbers, but how is the theorem that if
an equation has no solutions to some very large n, then it is true/false
holding water.

Jon Perry
perry@...
http://www.users.globalnet.co.uk/~perry/maths
BrainBench MVP for HTML and JavaScript
http://www.brainbench.com

-----Original Message-----
Sent: 01 June 2002 13:04
Subject: [PrimeNumbers] Re: Interesting page for the number crunchers

Standard Pellian analysis shows that
(x^4-1)/(x-1)=y^2
has no integer solution for
odd x in [9,10^20000]

The probabilty of a solution with
odd x > 10^20000 is about
1 part in 10^10000, so
I wouldn't advise "number crunching" :-)

David

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