Sums of powers (Jaroslaw Wroblewski)

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Part 1: Write 2005n as the sum of n-th powers of positive integers smaller than 2005 (as base). Minimize the number of summands. E.g. for 100 instead of 2005 and n=5 we can get a sum with 7 summands : 1005 = 995+525+375+295+275+225+145 Part 2: Write 2005^n as the sum of positive or negative n-th powers of positive integers other than 2005 as base. Minimize the number of summands. E.g. for 100 instead of 2005 and n=5 we can get a sum with 5 summands : 1005=1075-925+755+495-395 Decompose x^n as the sum of the smallest set of powers of n.