Abstract
In this note, we prove that there do not exist three consecutive powerful numbers, one of which is of the form \(x^{n}\pm 1\) and whose cubic square-free part (i.e., the unique square-free integer b such that the number can be written as \(a^{2}b^{3}\)) is either 1 or the product of distinct primes.
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Son, T.D. A remark on three consecutive powerful numbers. Acta Math. Hungar. (2026). https://doi.org/10.1007/s10474-026-01607-w
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DOI: https://doi.org/10.1007/s10474-026-01607-w