MathDB
x_n = n/(n+a)

Source: 1986 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p2

November 21, 2022
algebra

Problem Statement

Let aa be a given natural number and x1,x2,x3,...x_1, x_2, x_3, ... the sequence with xn=nn+ax_n = \frac{n}{n+a} (n∈N∗n \in N^* ). Prove that for every n∈N∗n \in N^* , the term xnx_n can be represented as the product of two terms of this sequence , and determine the number of representations depending on nn and aa.
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