On a conjecture of Erdos and Stewart
نویسنده
چکیده
For any k ≥ 1, let pk be the kth prime number. In this paper, we confirm a conjecture of Erdős and Stewart concerning all the solutions of the diophantine equation n! + 1 = pkp b k+1, when pk−1 ≤ n < pk.
منابع مشابه
Erdos Distance Problem in Vector Spaces over Finite Fields
The classical Erdos distance conjecture says that the number of distance determined by N points in Rd, d ≥ 2, is at least CN 2 d − . We shall discuss this problem in vector spaces over finite fields where some interesting number theory comes into play. A connection with the continuous analog of the Erdos distance conjecture, the Falconer distance conjecture will be also be established. Universi...
متن کاملCircular Averages and Falconer/erdos Distance Conjecture in the Plane for Random Metrics
We study a variant of the Falconer distance problem for perturbations of the Euclidean and related metrics. We prove that Mattila’s criterion, expressed in terms of circular averages, which would imply the Falconer conjecture, holds on average. We also use a diophantine conversion mechanism to prove that well-distributed case of the Erdos Distance Conjecture holds for almost every appropriate p...
متن کاملA Disproof of a Conjecture of Erdos in Ramsey Theory
Denote by kt(G) the number of complete subgraphs of order f in the graph G. Let where G denotes the complement of G and \G\ the number of vertices. A well-known conjecture of Erdos, related to Ramsey's theorem, is that Mmn^K ct(ri) = 2 ~*. This latter number is the proportion of monochromatic Kt's in a random colouring of Kn. We present counterexamples to this conjecture and discuss properties ...
متن کاملErdos Conjecture I
An old conjecture of Paul Erdos [6] states that there exist only 7 integers A. = 4,7,15.21,45,75 and 105 such that the difference A 28 is a prime for all B for which it is at least two. It is known that the conjecture is true for all A < 277 , as Cchiyama and Yorinaga have verified in 1977 ([21]), and in this short paper I show how it is related to other famous unsolved problems in prime number...
متن کاملAn old conjecture of Erdos-Turán on additive bases
There is a 1941 conjecture of Erdős and Turán on what is now called additive basis that we restate: Conjecture 0.1 (Erdős and Turán). Suppose that 0 = δ0 < δ1 < δ2 < δ3· · · is an increasing sequence of integers and
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Math. Comput.
دوره 70 شماره
صفحات -
تاریخ انتشار 2001