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- W4384832340 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 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 D. Furthermore, we give an upper bound for the period length of continued fraction expansion of 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 [MU]." @default.
- W4384832340 created "2023-07-21" @default.
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- W4384832340 date "2023-12-01" @default.
- W4384832340 modified "2023-10-16" @default.
- W4384832340 title "On continued fraction partial quotients of square roots of primes" @default.
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- W4384832340 doi "https://doi.org/10.1016/j.jnt.2023.06.013" @default.
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