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MMO 342 Moscow MO 1956 sequences with absolute values

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August 19, 2019
Sequenceabsolute valuealgebra

Problem Statement

Given three numbers x,y,zx, y, z denote the absolute values of the differences of each pair by x1,y1,z1x_1,y_1, z_1. From x1,y1,z1x_1, y_1, z_1 form in the same fashion the numbers x2,y2,z2x_2, y_2, z_2, etc. It is known that xn=x,yn=y,zn=zx_n = x,y_n = y, z_n = z for some nn. Find yy and zz if x=1x = 1.
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