Partition congruences

The number 4 can be partitioned in 5 ways. 1+1+1+1+1, 2+1+1, 2+2, 3+1, and 4. The number 9 can be partitioned in 30 ways and 14 in 135 ways. In fact, any number ending in 4 or 9 can be partitioned in x ways, where x is divisible by 5. The numbers 4, 9, and 14 are said to be congruent to each other.

This mathematical pattern has been observed by the genius Srinivasa Ramanujan decades ago. He found partition congruences for 5, 7 and 11. Recently, Karl Mahlburg, a PhD student at the University of Wisconsin in Madison, USA, generalized this theory on partition congruences. The new scientist magazine reports that his results have applications in particle physics and computer security.