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numbers around a circle

Source: OIFMAT II 2012 day 1 p1 - Chilean Math Forum FMAT Olympiad https://artofproblemsolving.com/community/c2484778_oifmat

September 27, 2021
combinatorics

Problem Statement

A circle is divided into n n equal parts. Marceline sets out to assign whole numbers from 1 1 to n n to each of these pieces so that the distance between two consecutive numbers is always the same. The numbers 887 887 , 217 217 and 1556 1556 occupy consecutive positions. How many parts was the circumference divided into?
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