MathDB
Process with pairs

Source: ARO Regional stage 2023 11.4

February 16, 2023
number theoryRussia

Problem Statement

We write pairs of integers on a blackboard. Initially, the pair (1,2)(1,2) is written. On a move, if (a,b)(a, b) is on the blackboard, we can add (−a,−b)(-a, -b) or (−b,a+b)(-b, a+b). In addition, if (a,b)(a, b) and (c,d)(c, d) are written on the blackboard, we can add (a+c,b+d)(a+c, b+d). Can we reach (2022,2023)(2022, 2023)?
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