论文标题
限制纤维序列模量的密度
Limiting density of the Fibonacci sequence modulo powers of a prime
论文作者
论文摘要
对于给定的Prime $ p $，我们确定fibonAcci序列获得的残基密度的限制为$λ\至\ infty $。特别是，我们表明，这种限制密度与Lucas Number Modulo $ P $的零有关。该证明使用fibonacci序列的分段插值与$ p $ - adic数字和墙壁信世基金会$ p $的表征，在$ p $ - addic的绝对值中，与$ p $ - 亚种黄金比率相关的数字。
For a given prime $p$, we determine the limit, as $λ\to \infty$, of the density of residues modulo $p^λ$ attained by the Fibonacci sequence. In particular, we show that this limiting density is related to zeros in the sequence of Lucas numbers modulo $p$. The proof uses a piecewise interpolation of the Fibonacci sequence to the $p$-adic numbers and a characterization of Wall-Sun-Sun primes $p$ in terms of the $p$-adic absolute value of a number related to the $p$-adic golden ratio.
