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Sequence

Source: 17-th Iranian Mathematical Olympiad 1999/2000

December 14, 2005
inductionnumber theory proposednumber theory

Problem Statement

A sequence of natural numbers c1,c2,…c_1, c_2,\dots is called perfect if every natural number mm with 1≤m≤c1+⋯+cn1\le m \le c_1 +\dots+ c_n can be represented as m=c1a1+c2a2+⋯+cnanm =\frac{c_1}{a_1}+\frac{c_2}{a_2}+\dots+\frac{c_n}{a_n} Given nn, find the maximum possible value of cnc_n in a perfect sequence (ci)(c_i).
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