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arXiv · 1004.4293

The art of juggling with two balls or A proof for a modular condition of Lucas numbers

Steve Butler
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Abstract

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.

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Steve Butler. 2010-04-28. The art of juggling with two balls or A proof for a modular condition of Lucas numbers. https://arxiv.org/abs/1004.4293

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