Abstract
Let parallel to center dot parallel to denote the distance to the nearest integer and, for a prime number p, let vertical bar center dot vertical bar(p) denote the p-adic absolute value. Over a decade ago, de Mathan and Teulie [Problemes diophantiens simultanes, Monatsh. Math. 143 (2004), 229-245] asked whether infq>A q center dot parallel to q alpha parallel to center dot vertical bar q vertical bar(p) = 0 holds for every badly approximable real number a and every prime number p. Among other results, we establish that, if the complexity of the sequence of partial quotients of a real number alpha grows too rapidly or too slowly, then their conjecture is true for the pair (alpha, p) with p an arbitrary prime.