In this paper we consider the following problem, which seems to have been brought to light fairly recently by M. Car. Can every sufficiently large integer n be expressed as n = p + ab with p prime and 1 ≤ a, b ≤ n½? Certainly one should expect this to be possible. Taking b = 1, for example, p will be restricted to the range n − n½ ≤ p < n, and this interval is conjectured to contain a prime, for large enough n. Alternatively, providing that n is not a square, we expect n = p + a2 to be solvable for sufficiently large n. However, although the statement that n = p + ab, with a, b ≤ n½, is far weaker than either of the aforementioned conjectures, it is nevertheless rather tricky to show that solutions must in fact exist.