# MATH

posted by
**intermediate player PLEASE HELP**
.

For what integer 0<n<1000, does the following system of n linear equations have no complex solution?

−10a1a1a1⋮a1+a2−10a2+a2+a2+a3+a3−10a3+a3+…+…+…+…+an+an+an−10an=9=99=999⋮=10n−1

Clarification: If the system always admits a solution, type your answer as 0. If there are multiple cases where the system doesn't admit a solution, type in any one of your answers.