Some unsolved problems in number theory
نویسندگان
چکیده
منابع مشابه
Some Solved and Unsolved Problems of Mine in Number Theory
I . Let p1 < p2 < . . . be the sequence of consecutive primes . Put pn+l pn = dn . It is well known that the sequence d o behaves very irregularly . An old result of Ricci and myself states that the set of limit points of d n /log n has positive measure . "It is of course clear to every right thinking person" that the set d o /log n is dense in (0, °O ) , but we are very far from being able to ...
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A k = max(p,+ t p,), k < p, < p, + , < 2k . In fact I cannot even disprove f(k) = Ak for all sufficiently large k, though it seems likely that f(k) > Ak for all large k. A well known theorem of Pólya and Störmer states that if u > uo(k) then u(u + 1) always contains a prime factor greater than k, thusf(k) can be determined in a finite number of steps, and an explicit bound has been given by Leh...
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Mathematics is full of unsolved problems. Many well educated people believe that mathematics is really a closed subject where everything is already known. Perhaps it would be good to explain already early in school how false this is. Let me illustrate this by the following example. At the international congress in Cambridge, England in 1912. Landau gave the talk in analytic number theory and he...
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Roger Fenn University of Sussex Department of Mathematics Sussex BN1 9RF, England [email protected] and Louis H. Kauffman Department of Mathematics, Statistics and Computer Science University of Illinois at Chicago 851 South Morgan St., Chicago IL 60607-7045, USA [email protected] and Vassily O. Manturov Moscow State University Department of Mechanics and Mathematics 119992, GSP-2,Leninskie Go...
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ژورنال
عنوان ژورنال: Resonance
سال: 1997
ISSN: 0971-8044,0973-712X
DOI: 10.1007/bf02836044