In the world of mathematics, partitioning a whole number means breaking it up into a sum. The simple idea of partitions has developed into a significant branch of number theory.
Partitions display intriguing patterns.
One can prove that for a given whole number, the number of partitions in which all the parts are odd always equals the number of partitions in which all the parts are distinct. Leonhard Euler established this theorem in the eighteenth century. One aspect of particular interest in the theory of partitions involves counting the number of different sums that generates a given positive integer. It turns out to be relatively straightforward to compute values of the partition function without having to write out all the sums. The integer 200, for instance, has 3,972,999,029,388 partitions.