Abstract | In vol. 32 of this Journal, G.E. Collins reported on extensive calculations supporting his conjecture that the exponent 1 − n in the well-known Mahler–Mignotte bound for the root separation of squarefree integral polynomials of degree n might be replaceable with − n / 2 . This paper exhibits infinite sequences of cubic polynomials with ‘true’ exponent − 2 , thus disproving that conjecture for degree n = 3 , and extends this to analogous bounds for close root triplets of quartic polynomials. |