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

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

2010-04-24

arxiv.org/abs/1004.4293v2

Mathematics

Combinatorics

4 pages; replaces previous version and adds references to similar existing proofs

Scientific paper

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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