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all sets of n consecutive integers {a+1,a+2,...,a+n} in which one =sum of others

Source: 2021 Ukraine NMO 10.5

April 4, 2021
number theorySum

Problem Statement

Find all sets of n≥2n\ge 2 consecutive integers {a+1,a+2,...,a+n}\{a+1,a+2,...,a+n\} where a∈Za\in Z, in which one of the numbers is equal to the sum of all the others.
(Bogdan Rublev)
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