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Find all 2002-tuples s.t. the sum equals 2002b^b

Source: Austrian Mathematical Olympiad 2002, Part 2, D1, P2

June 25, 2011
number theory proposednumber theory

Problem Statement

Let bb be a positive integer. Find all 20022002−tuples (a1,a2,…,a2002)(a_1, a_2,\ldots , a_{2002}), of natural numbers such that ∑j=12002ajaj=2002bb.\sum_{j=1}^{2002} a_j^{a_j}=2002b^b.
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