MathDB

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

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