The polynomial part of a restricted partition function related to the Frobenius problem.

Beck, Matthias; Gessel, Ira M.

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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...