Mathematical and Physical Journal
for High Schools
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Problem A. 501. (February 2010)

A. 501. Let p>3 be a prime. Determine the last three digits of


\sum_{i=1}^{p} \binom{i\cdot p}{p}\cdot\binom{(p-i+1)p}{p}

in the base-p numeral system.

(Based on the proposal of Gábor Mészáros, Kemence)

(5 pont)

Deadline expired on March 10, 2010.


Statistics:

12 students sent a solution.
5 points:Ágoston Tamás, Bodor Bertalan, Éles András, Frankl Nóra, Mester Márton, Nagy 235 János, Nagy 648 Donát, Somogyi Ákos, Strenner Péter, Szabó 928 Attila, Weisz Ágoston.
4 points:Backhausz Tibor.

Problems in Mathematics of KöMaL, February 2010