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Büchi’s problem in modular arithmetic for arbitrary quadratic polynomials. (English) Zbl 1450.11011

Let \(p\ge 5\) be prime, and let \(s\ge 1\) be an integer. Let \(f\) be any quadratic polynomial with coefficients in the ring of integers modulo \(p^s\), such that \(f\) is not a square. Suppose that \((f(1),f(2),\ldots ,f(N))\) is a sequence of squares modulo \(p^s\). In the article under review, the authors prove that there exists an integer \(M\) such that \(N\le M\). This article extends earlier work of the authors. The methods are elementary.

MSC:

11B50 Sequences (mod \(m\))
11B83 Special sequences and polynomials
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References:

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