MathDB

two binomials leave the same remainder when divided by 2

Source: Czech-Polish-Slovak Match 2014 day 2 P2

October 6, 2017

number theorybinomial coefficientsmodular arithmeticremainder

Problem Statement

Let all positive integers

n

satisfy the following condition: for each non-negative integers

k, m

with

k + m \le n

, the numbers

\binom{n-k}{m}

and

\binom{n-m}{k}

leave the same remainder when divided by

2

.
(Poland)
PS. The translation was done using Google translate and in case it is not right, there is the original text in Slovak