On continued fraction partial coefficients of square roots of primes

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10472027" target="_blank" >RIV/00216208:11320/23:10472027 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=EiBrvg3CXi" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=EiBrvg3CXi</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jnt.2023.06.013" target="_blank" >10.1016/j.jnt.2023.06.013</a>

Result language
angličtina
Original language name
On continued fraction partial coefficients of square roots of primes
Original language description
We show that for each positive integer a there exist only finitely many prime numbers p such that a appears an odd number of times in the period of continued fraction of '/p or '/2p. We also prove that if p is a prime number and D = p or 2p is such that the length of the period of continued fraction expansion of '/D is divisible by 4, then '/1 appears as a partial quotient in the continued fraction of length of continued fraction expansion of '/ D. Furthermore, we give an upper bound for the period D, where D is a positive non-square, and factorize some family of polynomials with integral coefficients connected with continued fractions of square roots of positive integers.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GM21-00420M" target="_blank" >GM21-00420M: Universal Quadratic Forms and Class Numbers</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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