Mathematical and Physical Journal
for High Schools
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Problem A. 457. (May 2008)

A. 457. Prove that, for every odd prime p,

\sum_{i=1}^{p-1}{2^i i^{p-2}}- \sum_{i=1}^{\frac{p-1}{2}}{i^{p-2}}

is divisible by p.

(5 pont)

Deadline expired on June 16, 2008.


5 students sent a solution.
5 points:Lovász László Miklós, Nagy 235 János, Tomon István, Wolosz János.
0 point:1 student.

Problems in Mathematics of KöMaL, May 2008