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In this short note we look at the problem of counting juggling patterns withone ball or two balls with a throw at every occurrence. We will do this forboth traditional juggling and for spherical juggling. In the latter case wewill show a connection to the "associated Mersenne numbers" (A001350) and so asa result will be able to recover a proof that the $p$th Lucas number iscongruent to 1 modulo p when p is a prime.

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