I am working on a paper and I am wondering if there's any mathematical theorem that says a system of nonlinear equations has infinite many complex (or real) solutions when there are m equations and n unknowns and m<n. I know that there is a theorem for polynomial set of equations regarding this (it says that in this case the problem is either inconsistent or there are infinite many complex solutions), but if anyone can suggest a reference I can look up, I'd appreciate it. Also, I am looking for proving that there "does" exist infinite many solutions, so if there's any assumption on the nonlinear set of equations (whether on the structure of it or a subset of nonlinear equations) it's ok and I'd appreciate the recommendation. Thanks y'all! PS: For the polynomial case, I've seen the statement only on Wikipedia here at : Wikipedia under section "Basic properties and definitions" with no reference. If anyone knows a reference that states this theorem formally please share it.
2026-03-26 12:47:51.1774529271
Is there any theorem that says "a nonlinear system of equations with less equations rather than unknowns has infinite complex solutions"?
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