MathDB

Hard NT Problem

Source: Azerbaijan Math Olympiad Training

December 15, 2019

number theoryTST

Problem Statement

Consider an odd prime number

p

and

p

consecutive positive integers

m_1,m_2,…,m_p

. Choose a permutation

\sigma

of

1,2,…,p

. Show that there exist two different numbers

k,l\in{(1,2,…,p)}

such that

p\mid{m_k.m_{\sigma(k)}-m_l.m_{\sigma(l)}}

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