1. For the origins of these types of questions, see P. Erdős: Summa Brasiliensis Math. II (1950), pp. 113–123.
2. P. Erdős, E. Szemerédi: Acta Arithmetica
15 (1968), pp. 85–90.
3. See the article by P. Erdős referred to in footnote 3, and also S. L. G. Choi: Mathematics of Computation
25 (1971) pp. 885–895.
4. Lifsic’s proof appears as the solution to Problem 143, p. 43 and pp. 159–161 in N. B. Vasil’ev, A. A. Egorov: Zadachi vsesoyuznikh matematicheskikh Olimpiad (Problems of the All-Soviet-Union Mathematical Olympiads), Nauka, Moscow, 1988 (in Russian).
5. For a proof of Dirichlet’s theorem we refer the reader to H. Rademacher: Lectures on Elementary Number Theory, Blaisdell Publ. Co., New York 1964. Cf. Chapter 14, pp. 121–136.