Sentence:  Finally in §5 we give one application to the curve "X"4 + "Y"4 = "Z"4, showing that the height inequalities for the curve imply the asymptotic Fermat conjecture and a weak form of the Masser-Oesterlé <WSD>"abc" conjecture</WSD>. 
Meaning of the word marked with <WSD> tags:  Given coprime positive integers "a", "b" and "c", such that "a" + "b" = "c", and "d" the radical of "abc" (the product of its distinct prime factors), the conjecture that "d" is usually not much smaller than "c" (in other words, that if "a" and "b" are divisible by large powers of primes, then "c" usually is not).