Unsolved Problem 18:
Are there distinct positive integers, a, b, c, and, d
such that a^5+b^5=c^5+d^5?
It is known that 1^3+12^3=9^3+10^3 and
133^4+134^4=59^4+158^4, but no similar relation
is known for fifth powers.
Other remarkable identities are
Diophantine Equation of Degree 5
- [Guy 1994]
- Richard K. Guy,
Unsolved Problems in Number Theory, second edition.
Springer Verlag. New York: 1994.
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.