A powerful number is a positive integer such that every prime that appears in its prime factorization appears there at least twice. Erdős, Mollin and Walsh conjectured that three consecutive powerful numbers do not exist. This paper shows that if they do exist, the smallest of the three numbers must have remainder 7, 27, or 35 when divided by 36.
"On Consecutive Triples Of Powerful Numbers,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 20:
2, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol20/iss2/3