Fifteen problems in number theory.

Pethö, Attila

Displaying similar documents to “Fifteen problems in number theory.”

Perfect powers with all equal digits but one.

Kihel, Omar, Luca, Florian (2005)

Journal of Integer Sequences [electronic only]

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Diophantine equations with linear recurrences An overview of some recent progress

Umberto Zannier (2005)

Journal de Théorie des Nombres de Bordeaux

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We shall discuss some known problems concerning the arithmetic of linear recurrent sequences. After recalling briefly some longstanding questions and solutions concerning zeros, we shall focus on recent progress on the so-called “quotient problem” (resp. " $d$ -th root problem"), which in short asks whether the integrality of the values of the quotient (resp. $d$ -th root) of two (resp. one) linear recurrences implies that this quotient (resp. $d$ -th root) is itself a recurrence. We shall also...