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Integers with determinant \pm 1

Source: INMO 2021 Problem 1

March 7, 2021

determinantIntegersnumber theoryINMO

Problem Statement

Suppose

r \ge 2

is an integer, and let

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

be

2r

integers such that

i

for any two integers

i

and

j

satisfying

1 \le i<j \le r

. Determine the maximum possible value of

r

.
Proposed by B Sury

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