Publications of (and about) Paul Erdös
Autor: Erdös, Pál
Title: On a problem in elementary number theory and a combinatorial problem (In English)
Source: Math. Comput. 18, 644-646 (1964).
Review: Let ft(n) denote the smallest integer k such that if 1 \leq a1 < a2 < ··· < ak \leq n, k = ft(n), is an arbitrary sequence of integers one can always find ai1, ai2,...,ait which have pairwise the same greatest common divisor. The author proved (cf. the preceding review) that for fixed t, ft(n) < n/\exp [(log n) ½]-\epsilon. In the present paper he proves that for every t and \epsilon > 0 there is an n0 so that for all n > n0(t,\epsilon), 2ct log n/ log log n < ft(n) < n3/4+\epsilon.
Classif.: * 11B83 Special sequences of integers and polynomials
Index Words: number theory
© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag