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- W4320499045 abstract "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 $sqrt{p}$ or $sqrt{2p}$. 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 $sqrt{D}$ is divisible by $4$, then $1$ appears as a partial quotient in the continued fraction of $sqrt{D}$. Furthermore, we give an upper bound for the period length of continued fraction expansion of $sqrt{D}$, 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. These results answer several questions recently posed by Miska and Ulas." @default.
- W4320499045 created "2023-02-14" @default.
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- W4320499045 date "2022-12-14" @default.
- W4320499045 modified "2023-09-26" @default.
- W4320499045 title "On continued fraction partial quotients of square roots of primes" @default.
- W4320499045 doi "https://doi.org/10.1016/j.jnt.2023.06.013" @default.
- W4320499045 hasPublicationYear "2022" @default.
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