Someone posted a question to sci.math.research on the Erdos-Turan conjecture: ---------------------------------------------------------- If for a subset S of the positive integers satisfies (*): (*) Its sum of reciprocals diverges. Then S contains arbitrarily long arithmetic progressions. ---------------------------------------------------------- The celebrated Green-Tao theorem proves this is true if S is the set of primes. Apparently it is not even known if (*) is sufficient to guarantee one single arithmetic progression of length 3 (!). Can anyone say what *is* known about this conjecture? --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele