论文标题
Schreier数字和非平凡的小除数，满足秩序的线性复发，最多两个
Schreier Numbers and Nontrivial Small Divisors Satisfying Linear Recurrence of Order at Most Two
论文作者
论文摘要
自Jozef Schreier于1930年首次引入以来，Schreier集成为研究对象，以构建Banach的猜想的反例。 1974年，乔治·安德鲁斯（George Andrews）发现了这些集合与斐波那契数之间的有趣联系，从那时起，Chu，Beanland和Finch-Smith证明了更多组合风味的结果。同时，伊安努奇（Iannucci）引入了一个小的除数的概念，并表征了所有自然数，其小除数在算术中，结果是由chentouf和chu概括的。然后结合了这两个想法，Chu介绍了Schreier编号的概念，一个schreier编号的概念是一个非平凡的小除数集（不超过1的小除数）是Schreier。我们的主要结果是双重的：我们首先证明了这些数字的渐近密度为0，并且有无限的许多非PRIME SCHREIER对，差异为2或4。然后是由于Chu对Iannucci的概括的概括而动机，我们对所有自然数量的表征都表征了所有非琐事的小型小型次数，使得无需订单，而无需大于较大的命令。
Schreier sets have been an object of study since first introduced in 1930 by Jozef Schreier to construct a counterexample to a conjecture of Banach. In 1974 George Andrews found interesting connections between these sets and Fibonacci number, and since then more results of a combinatorial flavor were proven by Chu, Beanland, and Finch-Smith. In parallel Iannucci introduced the concept of a small divisor and characterized all natural numbers whose small divisors are in arithmetic progression, results which were generalized by Chentouf and Chu. Then combining these two ideas, Chu introduced the notion of a Schreier number, one whose nontrivial small divisor set (small divisors excluding 1) is Schreier. Our main results are twofold: we first prove the asymptotic density of these numbers is 0 and that there are infinitely many non-prime Schreier pairs with difference 2 or 4. Then motivated by Chu's generalization of Iannucci's result we characterize all natural numbers whose nontrivial small divisors satisfy a linear recurrence with order no larger than 2.
