Consider the infinite system S of word equations {x"0u"1^ix"1u"2^ix"2...u"m^ix"m=y"0v"1^iy"1v"2^iy"2...v"n^iy"n|i@?N}. For each k@?N, let T"k be the subsystem of S given by i@?{k,k+1,k+2}. We prove two properties of the above system. (1)Let k>=1. If @f is a solution of T"k such that primitive roots of @f(u"1),@f(u"2),...,@f(u"m) are of equal length, as well as primitive roots of @f(v"1),@f(v"2),...,@f(v"n), then @f is a solution of the whole S. (2)If n=1 then, for any k>=2, a solution @f of T"k is also a solution of S.
['tpán Holub', 'Juha Kortelainen']
On systems of word equations with simple loop sets