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2

Part of 1973 Dutch Mathematical Olympiad

Problems(1)

exactly one sequence of 2n + 1 consecutive numbers

Source: Netherlands - Dutch NMO 1973 p2

1/27/2023
Prove that for every nāˆˆNn \in N there exists exactly one sequence of 2n+12n + 1 consecutive numbers, such that the sum of the squares of the first n+1n+1 numbers is equal to the sum of the squares of the last nn numbers. Also express the smallest number of that sequence in terms of nn.
consecutivenumber theorycombinatorics