1

Part of 2021 India National Olympiad

Problems(1)

Integers with determinant \pm 1

Source: INMO 2021 Problem 1

r \ge 2

is an integer, and let

m_1, n_1, m_2, n_2, \dots, m_r, n_r

2r

integers such that

\left|m_in_j-m_jn_i\right|=1

for any two integers

i

j

1 \le i<j \le r

. Determine the maximum possible value of

r

.
Proposed by B Sury

determinantIntegersnumber theoryINMO