Problem

Source: 239 MO 2024 J8

Tags: combinatorics



Let x1,x2, be a sequence of 0,1, such that it satisfies the following three conditions: 1) x2=x100=1, xi=0 for 1i100 and i2,100; 2) x2n1=xn50+1,x2n=xn50 for 51n100; 3) x2n=xn50,x2n1=xn50+xn100 for n>100. Show that the sequence is periodic.