Proving it is impossible; on Erd\H{o}s problem $\# 278$

Erd\H{o}s asked many mathematical questions. Some lead to exciting research, others turned out to be easily solved. In this article, we provide evidence that one of his questions, Erd\H{o}s problem \#278 , has no general answer. We do so by relating it with a hard knapsack problem instance,and by demonstrating that different, non-equivalent formulas arise depending on the structure of the moduli.