The Number of Partitions into Odd Parts Equals the Number of Partitions into Distinct Parts

In 1748 Euler proved that for any the number of partitions of into odd parts is the same as the number of partitions of into distinct parts This Demonstration shows how to go from either type to the other and back A partition of 6 for example is a sum like with parts The four partitions of into parts all of which are odd are and The four partitions of into parts that are distinct are

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