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Sequence of integers

Source: Romania TST 1995

September 18, 2009
number theory proposednumber theory

Problem Statement

The sequence (xn) (x_n) is defined by x_1\equal{}1,x_2\equal{}a and x_n\equal{}(2n\plus{}1)x_{n\minus{}1}\minus{}(n^2\minus{}1)x_{n\minus{}2} ∀n≥3 \forall n \geq 3, where a∈N∗ a \in N^*.For which value of a a does the sequence have the property that xi∣xj x_i|x_j whenever i<j i<j.
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