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 Problem 22: Triangles with Integer Sides, Medians, and Area 21-May-1995 Problem 21: Sum of Seven Cubes 14-May-1995 Problem 20: Primes of the Form n^2+1 7-May-1995 Problem 19: Pushing Discs Together 30-Apr-1995 Problem 18: Diophantine Equation of Degree 5 23-Apr-1995 Problem 17: Lattice Points Covered by a Set 16-Apr-1995 Problem 16: A Billiards Problem (revised) 9-Apr-1995 Problem 15: Square Free Mersenne Numbers 2-Apr-1995 Problem 14: A Series involving 1/n^3 26-Mar-1995 Problem 13: Rational Distances to the Vertices of a Square 19-Mar-1995 Problem 12: Graceful Trees 12-Mar-1995 Problem 11: Odd Perfect Numbers 5-Mar-1995 Problem 10: Egyptian Fractions 26-Feb-1995 Problem 9: Tiling the Unit Square 19-Feb-1995 Problem 8: pi+e 12-Feb-1995 Problem 7: Magic Knight's Tour 5-Feb-1995 Problem 6: Prime Fibonacci Numbers 29-Jan-1995 Problem 5: Goldbach's Conjecture 22-Jan-1995 Problem 4: Equichordal Points 15-Jan-1995 Problem 3: The Rational Box 8-Jan-1995 Problem 2: Twin Primes Conjecture 1-Jan-1995 Problem 1: Catalan's Conjecture

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