MathDB
x_1 =|a- b|, y_1 = |b-c|, z_1 = |c-d|, t_1 = |d -a|, sequence

Source: 2016 Saudi Arabia Pre-TST Level 4+ 2.2

September 13, 2020
algebraSequence

Problem Statement

Given four numbers x,y,z,tx, y, z, t, let (a,b,c,d)(a, b, c, d) be a permutation of (x,y,z,t)(x, y, z, t) and set x1=∣a−b∣x_1 =|a- b|, y1=∣b−c∣y_1 = |b-c|, z1=∣c−d∣z_1 = |c-d|, and t1=∣d−a∣t_1 = |d -a|. From x1,y1,z1,t1x_1, y_1, z_1, t_1, form in the same fashion the numbers x2,y2,z2,t2x_2, y_2, z_2, t_2, and so on. It is known that xn=x,yn=y,zn=z,tn=tx_n = x, y_n = y, z_n = z, t_n = t for some nn. Find all possible values of (x,y,z,t)(x, y, z, t).
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