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More on the distribution of the Fibonacci numbers modulo \(5c\)
2001Summary: The Fibonacci sequence \(F_0=0\), \(F_1=1\) and \(F_n=F_{n-1}+F_{n-2}\) for \(n\geq 2\) is purely periodic modulo \(m\) with \(2\leq m\in \mathbb N\). Take any shortest full period and form a frequency block \(B_m\in \mathbb N^m\) to consist of the residue frequencies within any full period.
openaire +2 more sources
Hypocycloids, Continued Fractions, and Distribution Modulo One
The American Mathematical Monthly, 1991openaire +1 more source
On the distribution of \(\alpha p^3\) modulo one
By means of the sieve methods developed by \textit{C. Jia} [J. Number Theory 45, 241-253 (1993; Zbl 0786.11042)] and \textit{R. C. Baker, G. Harman} and \textit{J. Rivat} [J. Number Theory 50, 261-277 (1995; Zbl 0822.11062)], the author proves: Let \(\alpha\) be any irrational number.openaire +2 more sources
Uniform distribution and sum modulo m of independent random variables
Statistics and Probability Letters, 1993exaly
On the uniform distribution modulo one of some subsequences of polynomial sequences
Journal of Number Theory, 1978exaly
On the uniform distribution modulo one of subsequences of polynomial sequences II
Journal of Number Theory, 1980exaly