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numbers 1-16 in a line, not circle - All-Russian MO 1997 Regional (R4) 8.1

Source:

September 23, 2024
number theoryPerfect Squarecombinatorics

Problem Statement

Prove that the numbers from 11 to 1616 can be written in a line, but cannot be written in a circle so that the sum of any two adjacent numbers is square of a natural number.