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numbers 1, 2,...,2012 in a circle

Source: 2013 Saudi Arabia IMO TST I p4

July 23, 2020
number theorycombinatoricsremainder

Problem Statement

Determine whether it is possible to place the integers 1,2,...,20121, 2,...,2012 in a circle in such a way that the 20122012 products of adjacent pairs of numbers leave pairwise distinct remainders when divided by 20132013.
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