IMO 1979 LL BRA8

The sequence (an) of real numbers is defined as follows:

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IMO 1979 LL BRA8

Origin: BRA

Problem

The sequence (an) of real numbers is defined as follows: a1 = 1, a2 = 2 and an = 3an−1 −an−2, n \geq3. Prove that for n \geq3, an =  a2 n−1 an−2 

  • 1, where [x] denotes the integer p such that p \leqx < p + 1.