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Number Theory with sequences

Source: First JBMO TST of France 2020, Problem 4

March 4, 2020
number theory

Problem Statement

Let a0,a1,...a_0, a_1,... be a sequence of non-negative integers and b0,b1,...b_0, b_1,... be a sequence of non-negative integers defined by the following rule: bi=gcd(ai,ai+1)b_i=gcd(a_i, a_{i+1}) for every i=>0i=>0 Is it possible every positive integer to occur exactly once in the sequence b0,b1,...b_0, b_1,...
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