Summary: We examine certain representations of integers by prime powers. Specifically, we show that given two primes \(p\) and \(q\), every integer has a bounded number of representations of the form \(p^{\alpha} q^{\beta} +p^{\gamma} +q^{\delta}\), with \(\alpha, \beta, \gamma\) and \(\delta\) nonnegative integers. Furthermore, we show that apart from finitely many integers and integers within a short list of infinite families, no positive integer allows more than one representation of this form.