Explicit abc-conjecture and its applications

We state well-known abc-conjecture of Masser-Oesterl´e and its explicit version, popularly known as the explicit abcconjecture, due to Baker. Laishram and Shorey derived from the explicit abc-conjecture that (1.1) implies that c < N1.75. We give a survey on improvements of this result and its consequences. Finally we prove that c < N1.7 and apply this estimate on an equation related to a conjecture of Hickerson that a factorial is not a product of factorials non-trivially