关于Fibonomial三角形的一个猜想
A Conjecture concerning the Fibonomial Triangle
摘要：
Chen和Sagan已经证明了三角形具有模2和模3的分形性质。这两个素数都具有$p$的斐波那契入口点是$p+1$的性质。本文研究了模5的多项式三角形，用Knuth和Wilf的一个定理证明了该三角形在被5整除的情况下具有循环结构。虽然这一结果并不新鲜，我们的证明方法是新的，并提出了一个猜想的整除系数的一般素数$p$。我们给出了这类素数的必要条件，即Fibonacci入口点必须大于或等于$p$，并提供了数值证据证明猜想的有效性.最后，我们对进一步的研究方向进行了讨论。
英文摘要：
The fibonomial triangle has been shown by Chen and Sagan to have a fractal nature mod 2 and 3. Both these primes have the property that the Fibonacci entry point of $p$ is $p+1$. We study the fibonomial triangle mod 5, showing with a theorem of Knuth and Wilf that the triangle has a recurring structure under divisibility by five. While this result is not new, our method of proof is new and suggests a conjecture for the divisibility of a fibonomial coefficient by a general prime $p$. We give necessary conditions for such primes, namely that the Fibonacci entry point must be greater than or equal to $p$, and offer numerical evidence for the validity of the conjecture. Lastly, we conclude with a discussion concerning further directions of research.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
