1 results
Büchi’s Problem in Modular Arithmetic for Arbitrary Quadratic Polynomials
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 62 / Issue 4 / December 2019
- Published online by Cambridge University Press:
- 26 April 2019, pp. 876-885
- Print publication:
- December 2019
-
- Article
- Export citation
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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 
$M$.
