For relatively prime positive integers and , the authors consider the arithmetic progression . Define and let be any integer. In this paper they show that for integers and
In particular, letting yields an improvement to the best previous lower bound on (obtained by S. Hong and Y. Yang [Proc. Am. Math. Soc. 136, No. 12, 4111–4114 (2008; Zbl 1157.11001)]) for all but three choices of .