1. UNSOLVED PROBLEMS AND REWARDS By Clark Kimberling. Offers prizes for solutions of some problems in number theory. http://faculty.evansville.edu/ck6/integer/unsolved.html

Unsolved Problems and Rewards Stated below are a few challenging problems. If you are first to publish a solution, let me know, and collect your reward! 1. The Kolakoski sequence: This sequence is is identical to its own runlength sequence. Reward: $200.00 for publishing a solution of any one of the five problems stated in Integer Sequences and Arrays. The sequence originates in William Kolakoski , "Self generating runs, Problem 5304," American Mathematical Monthly 72 (1965) 674. For a proof that the Kolakoski sequence is not periodic, see the same Monthly See also Kolakoski Sequence (Eric Weisstein's The World of Mathematics 2. A Shuffle. Is every positive integer a term of this sequence: Reward: $300.00. To see how to generate the sequence, visit Kimberling Sequence (Eric Weisstein's The World of Mathematics For a discussion and variant of the problem, see Richard K. Guy Unsolved Problems in Number Theory, second edition , Springer-Verlag, 1994. The problem originates in C. Kimberling, Problem 1615

2. Favorite Unsolved Problems Alexandre Eremenko (Purdue University). Mainly in analysis. http://www.math.purdue.edu/~eremenko/

Alexandre Eremenko picture Mathematics Department, Purdue University 150 N. University Street West Lafayette, IN 47907-2067 OFFICE: Math 450 PHONE: (765)494-1975, FAX: (765)494-0548 EMAIL: eremenko@math.purdue.edu Math 511 Linear Algebra, Fall 2005 vita Papers and Recent preprints (available in ps and pdf format) Some unsolved problems Some solved problems Stories and problems about ODE, calculus and history of science. CO-AUTHORS: A. Atzmon, A. Baernstein II, I. N. Baker, W. Bergweiler (4), V. Boichuk, M. Bonk J. Clunie, N. Eremenko, A. Fryntov, B. Fuglede, A. Gabrielov (6), Yu. Gaida, A. A. Goldberg D. Hamilton, W. Hayman J. Langley L. Lempert, G. Levin (3), J. Lewis , T. Lyons, M. Lyubich S. Merenkov D. Novikov I.V. Ostrovskii (3), M.I. Ostrovskii, M. Petrika, J. Rossi (2), L. Rubel M. Shapiro, D. Shea, M. Sodin (16), A. Solynin, A. Vainshtein. (My Erdos number: is 2). OTHER SITES: Math Journals Price Crisis , Math Journals Price Survey . Free old and new journals on line: Acta math. Ann.Acad.Sci.Fenn Mathdoc (EMANI), Numdam Project Euclid MAG journal (Kharkov)

3. Unsolved Problems In OR unsolved problems in OR. This page contains a list of open problems that I find intriguing. They are not as difficult or as significant as the question of http://www.statslab.cam.ac.uk/~rrw1/research/unsolved.html

Unsolved Problems in OR This page contains a list of open problems that I find intriguing. They are not as difficult or as significant as the question of whether P does or not equal NP. But these are problems that are easy to state and understand, but whose solution has defied the efforts of good researchers over a number of years. Most of these problems are in the realm of stochastic optimization. I would love to see a solution to any of these problems. This page is under construction. I plan to write something about the following problems, and others, in due course. The bomber problem See description The rendezvous problem See description Search for a moving target See abstract Non-preemptive release of stochastic jobs to uniform machines See abstract The unimportance of inserted idle time in non-preemptive stochastic scheduling to minimize flow time on parallel machines home page

4. Some Unsolved Problems Of course, this is not a complete list of all unsolved problems in mathematics. For instance, I omitted those problems which everybody knows anyway (like http://www.math.unibas.ch/~winkel/problem.html

5. Unsolved Problems In Function Theory My favorite unsolved problems. Prize policies when applicable, a prize for the problem will be payed with a check in US dollars to the first person who http://www.math.purdue.edu/~eremenko/uns.html

My favorite unsolved problems Prize policies: when applicable, a prize for the problem will be payed with a check in US dollars to the first person who sends me a complete solution which I will verify and recognize as correct. GEOMETRIC FUNCTION THEORY AND POTENTIAL THEORY: ps pdf Some constants studied by Littlewood (Updated Oct 2002). ps pdf Exceptional set in Gross' Theorem. ps pdf "Hawaii Conjecture" (attributed to Gauss). ps pdf Does every universe contain a place where you can stay at rest? (Lee Rubel) $200 ps pdf Erdos' problem on the length of lemniscates (at least $200). DIFFERENTIAL EQUATIONS AND ITERATION IN THE COMPLEX DOMAIN: ps pdf Meromorphic functions satisfying certain differential equations (E. Hille) ps pdf Wandering domains of entire functions. TRANSCENDENTAL HOLOMORPHIC CURVES: ps pdf Modified Cartan's Conjecture. $300 ps pdf Holomorphic curves with few inflection points. $500 RATIONAL FUNCTIONS AND RATIONAL CURVES: ps pdf Rational curves with real inflection points. (B. and M. Shapiro, for more info, see F. Sottile's page

6. Unsolved Problems And Conjectures Regarding equal sums of like powers, compiled by Chen Shuwen. http://euler.free.fr/eslp/unsolve.htm

Equal Sums of Like Powers Unsolved Problems and Conjectures The Prouhet-Tarry-Escott Problem a k + a k + ... + a n k = b k + b k + ... + b n k k n Is it solvable in integers for any n Ideal solutions are known for n = 1, 2, 3, 4, 5, 6, 7, 8 ,9, 11 and no other integers so far. How to find new solutions for n = 10 and How to find the general solution for n The general solution is known for ( k = 1 ) ( k = 1, 2 ) ( k = 1, 2, 3 ) only. The complete symmetric solution have been found for ( k = 1, 2, 3, 4 ) How to find a new solution of the type ( k =1, 2, 3, 4, 5, 6, 7, 8 ) How to find non-symmetric ideal solutions of ( k =1, 2, 3, 4, 5, 6, 7, 8 ) and ( k =1, 2, 3, 4, 5, 6, 7, 8, 9 ) How to find a solution chain of the type ( k = 1, 2, 3, 4 ) a a a a a b b b b b c c c c c ( k = 1, 2, 3, 4 ) Solution chains are known for ( k = 1 ) ( k = 1, 2 ) ( k = 1, 2, 3 ) and ( k = 1, 2, 3, 4, 5 ) so far. Some other open problems are present on Questions by Lander-Parkin-Selfrige (1967) a k + a k + ... + a m k = b k + b k + ... + b n k Is ( k m n ) always solvable when m n k Is it true that ( k m n ) is never solvable when m n k For which k m n such that m n k is ( k m n ) solvable ?

7. Overview Of "Mathematician's Secret Room" unsolved problems in Number Theory. English and Japanese text by Hisanori Mishima. http://www.asahi-net.or.jp/~KC2H-MSM/mathland/overview.htm

Overview of "Mathematician's Secret Room" Challenges to the Unsolved Problems in Number Theory (May 17, 2004) (Chapter 2, 4, 9, 10, Appendix 1, 4 are translated in English. Other chapters are still written only in Japanese, sorry.) Chapter 4 : A solution of case n=52 for n=x +y +z was added. Chapter 2 : Search range for patterns not including zero were extended up to 10 . (May 17, 2004) (For patterns including zero, up to 10 were serached.) (June 04, 2001) : In Chapter 7, new results by Tomas Oliveira and Silva. Their web site is here ( 3x+1 conjecture verification results Chapter 0 : Opening Why I had an interest in Number Theory. Chapter 1 : 4/n = 1/a + 1/b + 1/c whether do there exist the natural number solutions of above equation, or not. I found the construction method of the parameterize solution from arbitrary solutions. That is, Theorem : Let A, B, C in N be a solution of following Diophantine equation, m/P=1/A+1/B+1/C, B=kP (m=4, 5, 6, 7, P=prime, k in N (i.e. 2 of A, B, C can be divisable by P) Define a, b, c, d, e, f, c', d' as

8. Unsolved Problem Of The Week Archive A list of unsolved problems published by MathPro Press during 1995. http://cage.rug.ac.be/~hvernaev/problems/archive.html

Unsolved Problem of the Week Archive Welcome to the archive for the Unsolved Math Problem of the Week Each week, for your edification, we publish a well-known unsolved mathematics problem. These postings are intended to inform you of some of the difficult, yet interesting, problems that mathematicians are investigating. We give a reference so that you can get more information about the topic. These problems can be understood by the average person. Nevertheless, we do not suggest that you tackle these problems, since mathematicians have been unsuccessfully working on these problems for many years. Should you wish to discuss aspects of these problems with others, one of the newsgroups, such as sci.math , might be the appropriate forum. 3-Sep-1995 Problem 36 : Primes of the form n^n+1 27-Aug-1995 Problem 35 : Must one of n points lie on n/3 lines? 20-Aug-1995 Problem 34 : Squares with Two Different Decimal Digits 13-Aug-1995 Problem 33 : Unit Triangles in a Given Area 6-Aug-1995 Problem 32 : Can the Cube of a Sum Equal their Product 30-Jul-1995 Problem 31 : Different Number of Distances 23-Jul-1995 Problem 30 : Sum of Four Cubes 16-Jul-1995 Problem 29 : Fitting One Triangle Inside Another 9-Jul-1995 Problem 28 : Expressing 3 as the Sum of Three Cubes 2-Jul-1995 Problem 27 : Factorial that are one less than a Square 25-Jun-1995 Problem 26 : Inscribing a Square in a Curve 18-Jun-1995 Problem 25 : The Collatz Conjecture 11-Jun-1995 Problem 24 : Primes Between Consecutive Squares 4-Jun-1995 Problem 23 : Thirteen Points on a Sphere 28-May-1995

9. Unsolved Problems -- From MathWorld Some prominent outstanding unsolved problems (as well as some which are not Classic texts on unsolved problems in various areas of mathematics are Croft http://mathworld.wolfram.com/UnsolvedProblems.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Foundations of Mathematics Mathematical Problems Unsolved Problems Unsolved Problems There are many unsolved problems in mathematics. Some prominent outstanding unsolved problems (as well as some which are not necessarily so well known) include 1. The Goldbach conjecture 2. The Riemann hypothesis 3. The 4. The conjecture that there exists a Hadamard matrix for every positive multiple of 4. 5. The twin prime conjecture (i.e., the conjecture that there are an infinite number of twin primes 6. Determination of whether NP-problems are actually P-problems 7. The Collatz problem 8. Proof that the 196-algorithm does not terminate when applied to the number 196. 9. Proof that 10 is a solitary number 10. Finding a formula for the probability that two elements chosen at random generate the symmetric group 11. Solving the

10. Unsolved Problems unsolved problems. You can contact Stephen C. Locke at LockeS@fau.edu. Several people have asked me about unsolved problems. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Unsolved Problems -- From MathWorld Full Reptend Prime Pillai s Conjecture Universal Turing Machine Gelfand s Question Poincaré Conjecture unsolved problems http://mathworld.wolfram.com/topics/UnsolvedProblems.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Foundations of Mathematics Mathematical Problems Unsolved Problems A-Sequence Guy's Conjecture Quasiperfect Number abc Conjecture ... Projective Plane

12. The Geometry Junkyard Open Problems unsolved problems. Naoki Sato lists several conundrums from elementary geometry and number theory. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. Welcome To Mathsoft s of some unsolved problems and numerous links to other collections.......Compiled by Steven Finch. http://www.mathsoft.com/mathresources/problems/

Company Press Room Partners Events ... Contact Us Print this page Sorry! Page Not Found! Sorry, but the file you requested does not currently exist on this server. The link you followed is either outdated or inaccurate. Privacy

14. Some Unsolved Problems they are all unsolved. Of course, this is not a complete list of all unsolved problems in mathematics. For instance, I omitted those problems http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

15. Unsolved Problems Including the list of 50 problems of Bondy and Murty with current status. Compiled by Stephen C. Locke. http://www.math.fau.edu/locke/unsolved.htm

Unsolved Problems You can contact Stephen C. Locke at LockeS@fau.edu Several people have asked me about unsolved problems. I will take the easy way out: see the list of 50 problems in Bondy and Murty . You can now see the list as it originally appeard in the the text, Graph Theory with Applications . (May, 2004: The authors are writing the next edition of the book.) Some of these problems have been solved (and thus the title is slightly incorrect) and I won't claim to be familiar with all current results. If you find that one of them has been solved (or even that some reasonable progress has been made), please e-mail me . Also, I'm not giving you all of the references in Bondy and Murty . You should get yourself a copy of that book (or look at the online version). Problems 26-56 Problems 57-61 Problems number above 50 on my list are from sources other than the Bondy and Murtry text. Bojan Mohar lists some additional graph theoretic problems. The reconstruction conjecture . (S.M. Ulam, 1960) 2. A graph

16. Clay Mathematics Institute Are there still unsolved problems about the numbers 1, 2, 3, 4, ?, public lecture by Barry Mazur with figures by William Stein. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

17. Mathsoft Mathsoft Unsolved Problems s of some unsolved problems and numerous links to other collections.......Compiled by Steven Finch. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

18. Unsolved Problems unsolved problems. You can contact Stephen C. Locke at LockeS@fau.edu. Several people have asked me about unsolved problems. I will take the easy way out http://www.math.fau.edu/locke/Unsolved.htm

Unsolved Problems You can contact Stephen C. Locke at LockeS@fau.edu Several people have asked me about unsolved problems. I will take the easy way out: see the list of 50 problems in Bondy and Murty . You can now see the list as it originally appeard in the the text, Graph Theory with Applications . (May, 2004: The authors are writing the next edition of the book.) Some of these problems have been solved (and thus the title is slightly incorrect) and I won't claim to be familiar with all current results. If you find that one of them has been solved (or even that some reasonable progress has been made), please e-mail me . Also, I'm not giving you all of the references in Bondy and Murty . You should get yourself a copy of that book (or look at the online version). Problems 26-56 Problems 57-61 Problems number above 50 on my list are from sources other than the Bondy and Murtry text. Bojan Mohar lists some additional graph theoretic problems. The reconstruction conjecture . (S.M. Ulam, 1960) 2. A graph

19. Open Problems List A collection of papers outlining unsolved problems maintained at Stony Brook. http://www.math.sunysb.edu/dynamics/open.html

Open Problems in Dynamical Systems Open problems in holomorphic dynamics Two lists of problems are currently available on-line: Conformal Dynamics Problem List Ed. by B. Bielefeld, IMS at Stony Brook Preprint 1990/1 and more recent Problems in Holomorphic Dynamics Ed. by B. Bielefeld and M. Lyubich, IMS at Stony Brook Preprint 92/7 In addition some open questions may be found in these surveys Open problems in dynamics in several complex variables is a part of Several complex variables problems list available from Several complex variables preprint server in Indiana. Please send your problems to Gregery Buzzard at gbuzzard@iu-math.math.indiana.edu Problems in Low-Dimensional Topology a 380 pages PostScript file edited by Rob Kirby contain some problems on Topological Dynamics. Topology of hyperbolic attractors. A problem submitted by Christian Bonatti. A collection maintained by Sergiy Kolyada and Michal Misiurewicz Is entropy effectively computable? A problem by John Milnor We are soliciting open problems in various areas of Dynamical Systems for posting on this page. You can post a problem by filling out this form or by sending an e-mail to webmaster@math.sunysb.edu

20. Open Problems For Undergraduates background, and may readily be understood and worked on by anyone who is eager to think about interesting and unsolved mathematical problems. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

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