A Lower Bound in the abc Conjecture, Original Research Article

We show that there exists an infinite sequence of sums P: a+b=c of rational integers with large height compared to the radical: h(P)greater-or-equal, slantedr(P)+4Kl image/log h(P) with Kl=2l/2 image>1.517 for l=0.5990. This improves the result of Stewart and Tijdeman [9]. The value of l comes from an asymptotic bound for the packing density of spheres. We formulate our result such that improved knowledge of l immediately improves the value of Kl.