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Sequence with primes - Argentina TST 2010

Source:

May 2, 2010
algebrapolynomialnumber theory unsolvednumber theory

Problem Statement

Let pp and qq be prime numbers. The sequence (xn)(x_n) is defined by x1=1x_1 = 1, x2=px_2 = p and xn+1=pxn−qxn−1x_{n+1} = px_n - qx_{n-1} for all n≥2n \geq 2. Given that there is some kk such that x3k=−3x_{3k} = -3, find pp and qq.
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