# Unsolved Problems in Number Theory

Part of the Unsolved Problems in Intuitive Mathematics book series (PBM, volume 1)

Part of the Unsolved Problems in Intuitive Mathematics book series (PBM, volume 1)

To many laymen, mathematicians appear to be problem solvers, people who do "hard sums". Even inside the profession we dassify ourselves as either theorists or problem solvers. Mathematics is kept alive, much more than by the activities of either dass, by the appearance of a succession of unsolved problems, both from within mathematics-itself and from the in creasing number of disciplines where it is applied. Mathematics often owes more to those who ask questions than to those who answer them. The solu tion of a problem may stifte interest in the area around it. But "Fermat's Last Theorem", because it is not yet a theorem, has generated a great deal of "good" mathematics, whether goodness is judged by beauty, by depth or byapplicability. To pose good unsolved problems is a difficult art. The balance between triviality and hopeless unsolvability is delicate. There are many simply stated problems which experts tell us are unlikely to be solved in the next generation. But we have seen the Four Color Conjecture settled, even ifwe don't live long enough to leam the status of the Riemann and Goldbach hypotheses, of twin primes or Mersenne primes, or of odd perfeet numbers. On the other hand, "unsolved" problems may not be unsolved at all, or may be much more tractable than was at first thought.

Arithmetic Mersenne prime Prime Prime number Zahlentheorie function mathematics number theory theorem

- DOI https://doi.org/10.1007/978-1-4757-1738-9
- Copyright Information Springer-Verlag New York 1981
- Publisher Name Springer, New York, NY
- eBook Packages Springer Book Archive
- Print ISBN 978-1-4757-1740-2
- Online ISBN 978-1-4757-1738-9
- Series Print ISSN 0941-3502
- About this book