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0342 number theory with sequence 3rd edition Round 4 p2

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May 9, 2021
number theory3rd edition

Problem Statement

The sequence {xn}n≥1\{x_n\}_{n\ge1} is defined by x1=7x_1 = 7, xn+1=2xn2−1x_{n+1} = 2x^2_n - 1, for all positive integers nn. Prove that for all positive integers nn the number xnx_n cannot be divisible by 20032003.
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