Arithmetic progressions in squarefull numbers

We answer a number of questions of Erdős on the existence of arithmetic progressions in [Formula: see text]-full numbers (i.e. integers with the property that every prime divisor necessarily occurs to at least the [Formula: see text]th power). Further, we deduce a variety of arithmetic constraints upon such progressions, under the assumption of the [Formula: see text]-conjecture of Masser and Oesterlé.