2

Part of 2003 Miklós Schweitzer

Problems(1)

Miklós Schweitzer 2003, Problem 2

Source: Miklós Schweitzer 2003

p

be a prime and let

M

n\times m

matrix with integer entries such that

Mv\not\equiv 0\pmod{p}

for any column vector

v\neq 0

whose entries are

0

1

. Show that there exists a row vector

x

with integer entries such that no entry of

xM

0\pmod{p}

.
(translated by L. Erdős)

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