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Chinese TST 2008 P2

Source:

April 3, 2008
inductionnumber theoryalgebraSequencerecurrence relation

Problem Statement

The sequence {xn} \{x_{n}\} is defined by x_{1} \equal{} 2,x_{2} \equal{} 12, and x_{n \plus{} 2} \equal{} 6x_{n \plus{} 1} \minus{} x_{n}, (n \equal{} 1,2,\ldots). Let p p be an odd prime number, let q q be a prime divisor of xp x_{p}. Prove that if q≠2,3, q\neq2,3, then q\geq 2p \minus{} 1.
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