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# Hurwitz equation

Given a length $k$ and a multiplier $m$, a Hurwitz equation 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

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## Mathematics Subject Classification

11J06*no label found*11D72

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