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Hint to puzzle 56: Partition identity

Let p(n) be the number of partitions of n.  So, for example, p(5) = 7.  Establish the following two results, for 1 less than or equal to i less than or equal to n−1.

  1. The number of partitions of n which have at least i 1s is p(n − i).
  2. The number of partitions of n in which i appears is p(n − i).