Publikace na Matematicko-fyzikální fakulta |
2023
Abstrakt
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.