MathDB
0731

Source:

May 12, 2008
modular arithmeticalgebrapolynomial

Problem Statement

Let p p be a prime and let d∈{0, 1, …, p} d \in \left\{0,\ 1,\ \ldots,\ p\right\}. Prove that \sum_{k \equal{} 0}^{p \minus{} 1}{\binom{2k}{k \plus{} d}}\equiv r \pmod{p}, where r \equiv p\minus{}d \pmod 3, r\in\{\minus{}1,0,1\}.
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