MathDB

3.1

Part of MathLinks Contest 7th

Problems(1)

0731

Source:

5/12/2008
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\}.
modular arithmeticalgebrapolynomial