Geodesic
Büchi’s Problem in Modular Arithmetic for Arbitrary Quadratic Polynomials
Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 876-885

Voir la notice de l'article provenant de la source Cambridge University Press

Given a prime $p\geqslant 5$ and an integer $s\geqslant 1$, 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 $(f(1),\ldots ,f(N))$ is a sequence of squares, then $N$ is at most $M$. We also provide some explicit formulas for the optimal $M$.
DOI : 10.4153/S0008439519000225
Mots-clés : Büchi sequence, Hensley sequence 
Sáez, Pablo; Vidaux, Xavier; Vsemirnov, Maxim. Büchi’s Problem in Modular Arithmetic for Arbitrary Quadratic Polynomials. Canadian mathematical bulletin, Tome 62 (2019) no. 4, pp. 876-885. doi: 10.4153/S0008439519000225
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     title = {B\"uchi{\textquoteright}s {Problem} in {Modular} {Arithmetic} for {Arbitrary} {Quadratic} {Polynomials}},
     journal = {Canadian mathematical bulletin},
     pages = {876--885},
     year = {2019},
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     doi = {10.4153/S0008439519000225},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439519000225/}
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