Hurwitz Equation

The Diophantine Equation

$${x_1}^2+{x_2}^2+\ldots+{x_n}^2=ax_1 x_2 \cdots x_n$$

which has no Integer solutions for $a>n$.

See also Lagrange Number (Diophantine Equation)

References

Guy, R. K. ``Markoff Numbers.'' §D12 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 166-168, 1994.