Solution: 2013-17 Repeated numbers

A real sequence \( x_1, x_2, x_3, \cdots \) satisfies the relation \( x_{n+2} = x_{n+1} + x_n \) for \( n = 1, 2, 3, \cdots \). If a number \( r \) satisfies \( x_i = x_j = r \) for some \( i \) and \( j \) \( (i \neq j) \), we say that \( r \) is a repeated number in this sequence. Prove that there can be more than \( 2013 \) repeated numbers in such a sequence, but it is impossible to have infinitely many repeated numbers.

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2 thoughts on “Solution: 2013-17 Repeated numbers

  1. 김홍규

    정답자에는 이름이 없고 점수는 올랐는데, 저 혹시 틀린건가요 맞춘건가요?

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