Mathematical and Physical Journal
for High Schools
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Problem A. 511. (May 2010)

A. 511. Show that for arbitrary positive integers n, k there exists a polynomial p(x), with degree at most $100\sqrt{nk}$ , such that $p(0) > \big(\big|p(1)\big|+\ldots+\big|p(n)\big|\big) + \big(\big|p(-1)\big|+\ldots+\big|p(-k)\big|\big)$ .

(5 pont)

Deadline expired on June 10, 2010.

Statistics:

1 student sent a solution.

5 points: Nagy 648 Donát.

Problems in Mathematics of KöMaL, May 2010