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Maximum exponent of prime dividing x_{2011}-1

Source: Baltic Way 2011

November 6, 2011
number theory proposednumber theory

Problem Statement

Let aa be any integer. Define the sequence x0,x1,…x_0,x_1,\ldots by x0=ax_0=a, x1=3x_1=3, and for all n>1n>1 xn=2xn−1−4xn−2+3.x_n=2x_{n-1}-4x_{n-2}+3. Determine the largest integer kak_a for which there exists a prime pp such that pkap^{k_a} divides x2011−1x_{2011}-1.
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