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| New Conditions on the Nagell-Ljunggren Equation xp−1/x−1=yq |
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Citation： |
Han CHEN,Preda MIH˘AILESCU.New Conditions on the Nagell-Ljunggren Equation xp−1/x−1=yq[J].Chinese Annals of Mathematics B,2026,(2):389~412 |
| Page view： 284
Net amount： 318 |
Authors： |
Han CHEN; Preda MIH?AILESCU |
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| Abstract： |
In this paper, the authors consider the equation xp?1/x?11=peyq, for distinct odd prime exponents p, q, and show that, for p>3, it has no solutions under the condition that q does not divide hp??, the minus part of the class number of the p-th cyclotomic field. |
Keywords： |
Nagell-Ljunggren conjecture Diophantine equations Class field theory |
Classification： |
11D61, 11R37 |
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