# Hurwitz equation

Given a length $k$ and a multiplier $m$, a for a set of integers $x_{1},x_{2},\ldots,x_{k}$ states that

 $\sum_{i=1}^{k}{x_{i}}^{2}=m\prod_{i=1}^{k}x_{i}.$

There is no solution to the equation if $m>k$. Solutions can sometimes be found for $m\leq k$ by starting from a $k$-long set of 1s. The Markov equation for the Markov numbers has $k=m=3$.

## References

• 1 R. K. Guy, Unsolved Problems in Number Theory New York: Springer-Verlag 2004: D12
Title Hurwitz equation HurwitzEquation 2013-03-22 17:26:13 2013-03-22 17:26:13 PrimeFan (13766) PrimeFan (13766) 4 PrimeFan (13766) Definition msc 11J06 msc 11D72