MathDB
a_{n+1} = a_n^2 + (a_n - 1)^2 , a_q - ap = a_m - a_k

Source: Austrian Polish 1981 APMC

April 26, 2020
Sequencerecurrence relationalgebrarational

Problem Statement

The sequence a0,a1,a2,...a_0, a_1, a_2, ... is defined by an+1=an2+(an−1)2a_{n+1} = a^2_n + (a_n - 1)^2 for n≥0n \ge 0. Find all rational numbers a0a_0 for which there exist four distinct indices k,m,p,qk, m, p, q such that aq−ap=am−aka_q - a_p = a_m - a_k.
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