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sum of every 5 consecutive numbers in a circle is multiple of 13

Source: Mathematics Regional Olympiad of Mexico Northeast 2018 P1

September 12, 2022
algebra

Problem Statement

NN different positive integers are arranged around a circle , in such a way that the sum of every 55 consecutive numbers in the circle is a multiple of 1313. Let AA be the smallest possible sum of the nn numbers. Calculate the value of AA for ∙\bullet n=99n = 99, ∙\bullet n=100n = 100.
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