 The multiplicative inverse of its generating function is the Euler function; by Euler's pentagonal number theorem this function is an alternating sum of pentagonal number powers of its argument.Srinivasa Ramanujan first discovered that the partition function has nontrivial patterns in modular arithmetic, now known as Ramanujan's congruences.For instance, whenever the decimal representation of formula_2 ends in the digit 4 or 9, the number of partitions of formula_2 will be divisible by 5.