On Gaps Between k-Free Numbers Original Research Article

An elementary proof is given that for k ≥ 3 there exists a constant c = c(k) such that for x sufficiently large (depending on k), the interval (x, x + cx1/(2k + 1) log x] contains a k-free number. This result improves on a previous result of M. Filaseta (J. Number Theory30, No. 2 (1988), 208-225).