olymmath

FKMO 2013 Problem 5

    Two coprime positive integers a,ba, b are given. Integer sequence {an},{bn}\{ a_n \}, \{b_n \} satisties (a+b2)2n=an+bn2(a+b \sqrt2 )^{2n} = a_n + b_n \sqrt2 Find all prime numbers pp such that there exist positive integer n≤pn \le p satisfying p∣bnp | b_n .

    Dataset text AI-MO AoPS. Quoted with source.

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