Mathematician untangles legendary problem

The strange numerical relationships Ramanujan discovered, now called the three Ramanujan "congruences," mystified scores of number theorists. During the Second World War, one mathematician and physicist named Freeman Dyson began to search for more elementary ways to prove Ramanujan's congruences. He developed a tool, called a "rank," that allowed him to split partitions of whole numbers into numerical groups of equal sizes. The idea worked with 5 and 7 but did not extend to 11. Dyson postulated that there must be a mathematical tool--what he jokingly called a "crank"--that could apply to all three congruences.
...Mahlburg found that instead of dividing numbers into equal groups, such as putting the number 115 into five equal groups of 23 (which are not multiples of 5), the partition congruence idea still holds if numbers are broken down differently. In other words, 115 could also break down as 25, 25, 25, 10 and 30. Since each part is a multiple of 5, it follows that the sum of the parts is also a multiple of 5. Mahlburg shows the idea extends to every prime number.