Ramanujan's congruences

Ramanujan's congruences describe surprising patterns in the partition function, which counts the ways to express a number as sums of positive integers. Specifically, he discovered that for certain numbers, the total count of partitions exhibits regularity when divided by specific values. For example, the number of partitions of 5k + 4 is always divisible by 5, meaning no remainder. Similarly, partitions for 7k + 5 are divisible by 7, and for 11k + 6 by 11. These patterns reveal deep, unexpected links between number theory and modular forms, highlighting remarkable regularities in seemingly complex counting problems.