Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
Already signed up?
New to KöMaL?

Problem A. 610. (February 2014)

A. 610. There is given a prime number \(\displaystyle p\) and two positive integers, \(\displaystyle k\) and \(\displaystyle n\). Determine the smallest nonnegative integer \(\displaystyle d\) for which there exists a polynomial \(\displaystyle f(x_1,\dots,x_n)\) on \(\displaystyle n\) variables, with degree \(\displaystyle d\) and having integer coefficients that satisfies the following property: for arbitrary \(\displaystyle a_1,\dots,a_n\in\{0,1\}\), \(\displaystyle p\) divides \(\displaystyle f(a_1,\dots,a_n)\) if and only if \(\displaystyle p^k\) divides \(\displaystyle a_1+\dots+a_n\).

(5 pont)

Deadline expired on March 10, 2014.


1 student sent a solution.
3 points:1 student.

Problems in Mathematics of KöMaL, February 2014