Banach matchboxes problem and a congruence for primes

Details Banach matchboxes problem and a congruence for primes Banach matchboxes problem and a congruence for primes

2011-10-26

arxiv.org/abs/1110.5686v1

Mathematics

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2 pages

Scientific paper

Using an identity arising in the known Banach probability problem on
matchboxes, we prove an unexpected congruence for odd prime $p:$ for $1\leq
k\leq \frac{p-1}{2},\enskip \sum_{i=1}^{p-2k-1}2^{i-1}\binom{k-1+i}{k}\equiv
0\pmod p.$

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