MathDB

An integer partition, is a way of writing n as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same partition. For example, 4 can be partitioned in five distinct ways: 4 3 + 1 2 + 2 2 + 1 + 1 1 + 1 + 1 + 1 The number of partitions of n is given by the partition function

p\left ( n \right )

. So

p\left ( 4 \right ) = 5

. Determine all the positive integers so that

p\left ( n \right )+p\left ( n+4 \right )=p\left ( n+2 \right )+p\left ( n+3 \right )

Problem Statement