Leo Tolstoy's charming short story Three Hermits (Три старца) of 1886 has frequently been cited in academic and popular works about prayer. I don't want to spoil the ending - the (short!) text can be readily found online in English and Russian. There's even a film dramatization in Притчи 2 (2011) (19m25 video). Tolstoy, a collector of folk tales, apparently did not originate this story, but adapted or expanded it from one he had heard.
In the 1961 translation by Gleb Struve (Russian Tales, Bantam Books, 1961) he remarks:
At the core of the legend lies a well-known subject, a variant of which can be found in St. Augustine. St. Augustine's version of the legend became known in Russia in the sixteenth century. It is unlikely, however, that Tolstoy used as his source any of the bookish versions; the legend probably came to him in an oral retelling. p165
Similarly, Donald Barthelme's short story At the Tolstoy Museum (New Yorker, 24 May 1969, p32ff), later collected in City Life (Farrar, Straus and Giroux, 1970), includes the lines:
[Three Hermits] is written in a very simple style. It is said to originate in a folktale. There is a version of it in St. Augustine.
It is not hard to find other people mentioning an Augustinian connection, but I haven't found anything more specific. "In St. Augustine" is not a very helpful citation, given the size of his corpus.
Does anyone know where Augustine's version of the story can be found (or indeed any non-Tolstoy version)? How does Tolstoy's retelling differ from his Russian sources or from Augustine's original, and do any of those differences relate to Tolstoy's specific Christian beliefs (for example, Christian anarchism and its rejection of church authority)?