MathDB
(a, 2ad+b, ad^2+bd+c)

Source: Moldova JTST 2023

May 5, 2023
combinatorics

Problem Statement

On the board there are three real numbers (a,b,c)(a,b,c). During a procedureprocedure the numbers are erased and in their place another three numbers a written, either (c,b,a)(c,b,a) or every time a nonzero real number d d is chosen and the numbers (a,2ad+b,ad2+bd+c)(a, 2ad+b, ad^2+bd+c) are written. 1) If we start with (1,−2,−1)(1,-2,-1) written on the board, can we have the numbers (2,0,−1)(2,0,-1) on the board after a finite number of procedures? 2) If we start with (1,−2,−1)(1,-2,-1) written on the board, can we have the numbers (2,−1,−1)(2,-1,-1) on the board after a finite number of procedures?
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