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A partition of a positive integer is even if all its elements are even numbers. Similarly, a partition is odd if all its elements are odd. Determine all positive integers

n

such that the number of even partitions of

n

is equal to the number of odd partitions of

n

. Remark: A partition of a positive integer

n

is a non-decreasing sequence of positive integers whose sum of elements equals

n

. For example,

(2; 3; 4), (1; 2; 2; 2; 2)

and

(9)

are partitions of

9.

Problem Statement