用两个球玩杂耍的艺术或Lucas数的模条件的证明
The art of juggling with two balls or A proof for a modular condition of Lucas numbers
摘要：
在这个简短的说明中，我们看看计数杂耍模式的问题，一个球或两个球，在每一次出现的投掷。我们将为传统的杂耍和球形杂耍做这件事。在后一种情况下，我们将展示与“相关联的梅森数”（A001350）的联系，从而能够证明当p是素数时，第$p$个卢卡斯数与1模p全等。
英文摘要：
In this short note we look at the problem of counting juggling patterns with one ball or two balls with a throw at every occurrence. We will do this for both traditional juggling and for spherical juggling. In the latter case we will show a connection to the "associated Mersenne numbers" (A001350) and so as a result will be able to recover a proof that the $p$th Lucas number is congruent to 1 modulo p when p is a prime.
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。
