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Erschienen in:
2008 | OriginalPaper | Buchkapitel
Class Number Conditions for the Diagonal Case of the Equation of Nagell and Ljunggren
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The diagonal case of the Nagell-Ljunggren equation is
(1)
$$ \frac{{x^p - 1}} {{x - 1}} = p^e \cdot y^p with x,y \in \mathbb{Z} e \in \left\{ {0,1} \right\}, $$
and
p
an odd prime. The only known nontrivial solution is
(2)
$$ \frac{{18^3 - 1}} {{18 - 1}} = 7^3 , $$
and it is conjectured to be also the only such solution. However, it is not even proved that (1) has only finitely many solution.
