23-Jul-1995
Unsolved Problem 30:
Is every integer the sum of four cubes?
Here we allow the cubes to be positive, negative, or zero.
For example, 84=0^3+41639611^3+(-41531726)^3+(-8241191)^3.
It is not known if 148, for example, is the sum of
four cubes.
Reference:
- [Guy 1994]
- Richard K. Guy,
Unsolved Problems in Number Theory, second edition.
Springer Verlag. New York: 1994.
Page 151.
Sum of Four Cubes
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 do not suggest that you tackle these problems,
since mathematicians have been unsuccessfully working on these
problems for many years.
general references
previous problem
problem archive
next problem
electronic publications