MathDB
x_1 = |x - y|, y_1 = | y -z|, z_1 = |z- x| , sequence

Source: 2016 Saudi Arabia Pre-TST Level 4 2.1

September 13, 2020
algebraSequence

Problem Statement

Given three numbers x,y,zx, y, z, and set x1=∣x−y∣,y1=∣y−z∣,z1=∣z−x∣x_1 = |x - y|, y_1 = | y -z|, z_1 = |z- x|. From x1,y1,z1x_1, y_1, z_1, form in the same fashion the numbers x2,y2,z2x_2, y_2, z_2, and so on. It is known that xn=x,yn=y,zn=zx_n = x, y_n = y, z_n = z for some nn. Find all possible values of (x,y,z)(x, y, z).
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