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Bagatela 15 m. 49, Warsaw 10, Poland. A. Makowski 4. The hypothesis put forward by G. H. Morley is not in fact correct, since the number 83,828,316,391 is divisible by 53. A reason for there being so many cases in which the hypothesis is verified is that numbers of the form (xp-ap)/(x-a), with x prime and prime to a are considerably restricted as to their possible factors-any factor must be of the form 2lep + 1, where h is an integer. To prove this let q(>p) be a prime dividing (xp-ap)/(x-a) and, working modulo q, let b be such that x == ab. Then (ab)p = ap whence bp = 1 if q is prime to a. By Fermat's Theorem 6a_1 = 1 and so p divides q-1. Hence q-1 = mp and, since q is odd, m is even.

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Abstract.Suppose /'is a bounded analytic function on the unit disc whose Fatou boundary function is approximately continuous from above at 1 with value 0. It is well known that /'tends to zero radially and therefore along every nontangential arc. Tanaka [3] and Boehme and Weiss [1] have shown that / must also tend to zero along certain arcs which are tangential from above. The purpose of this paper is to improve their results by producing a larger collection of such tangential arcs along which /'tends to zero. We construct a class of examples to show that our result is actually better.