MathDB
even partitions = odd partitions, sum of even numbers is n

Source: IMOC 2019 C1

August 19, 2021
combinatoricspartitionDistributionscombinatorics solvedParity

Problem Statement

Given a natural number nn, if the tuple (x1,x2,…,xk)(x_1,x_2,\ldots,x_k) satisfies 2∣x1,x2,…,xk2\mid x_1,x_2,\ldots,x_k x1+x2+…+xk=nx_1+x_2+\ldots+x_k=n then we say that it's an even partition. We define odd partition in a similar way. Determine all nn such that the number of even partitions is equal to the number of odd partitions.
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