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Sequence with cubes

Source: OME 2014 4

July 16, 2014
geometrynumber theory unsolvednumber theory

Problem Statement

Let (xn)(x_n) be a sequence of positive integers defined by x1=2x_1=2 and xn+1=2xn3+xnx_{n+1}=2x_n^3+x_n for all integers n≥1n\ge1. Determine the largest power of 55 that divides x20142+1x_{2014}^2+1.
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