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Goormaghtigh conjecture

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Revision as of 22:15, 28 April 2009 by Vipul (talk | contribs) (Created page with '==Statement== The equation: <math>\frac{x^m - 1}{x - 1} = \frac{y^n - 1}{y-1}</math>, has the following integer solutions for <math>x,y > 1</math> and <math>m,n > 2</math>: *...')

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Statement

The equation:

$\frac{x^{m} - 1}{x - 1} = \frac{y^{n} - 1}{y - 1}$ ,

has the following integer solutions for $x, y > 1$ and $m, n > 2$ :

$(x, y, m, n) = (5, 2, 3, 5)$ .
$(x, y, m, n) = (90, 2, 3, 13)$ .

Related facts and conjectures

Feit-Thompson conjecture

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