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Preprint Number 1610

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1610. Pablo Sáez, Xavier Vidaux and Maxim Vsemirnov
Optimal bounds for Büchi's problem in modular arithmetic II

Submission date: 4 May 2019


accepted in Canadian Mathematical Bulletin
Given a prime p ≥ 5 and an integer s ≥ 1, we show that there exists an integer M such that for any quadratic polynomial f with coefficients in the ring of integers modulo p^s, such that f is not a square, if a sequence (f(1), ... ,f(N)) is a sequence of squares, then N is at most M. We obtain this result by reducing to the case where f has an invertible dominant coefficient.

Mathematics Subject Classification: 11B50, 11T99, 12Y05

Keywords and phrases:

Full text arXiv 1905.01411: pdf, ps.

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