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.
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