Bezout's Theorem
In general, two algebraic curves of degrees 
and 
intersect in 
points and cannot meet in more than points unless they have a component in common (i.e., the equations defining them have a common factor). Thiscan also be stated: if 
and 
are two Polynomials with no roots in common, then thereexist two other Polynomials 
and 
such that 
. Similarly, given
Polynomial equations of degrees 
, 
, ...
in variables, there are in general 
common solutions.
References
Coolidge, J. L. A Treatise on Algebraic Plane Curves. New York: Dover, p. 10, 1959.
- Study's Theorem
- Sturm Chain
- Sturm Function
- Sturmian Separation Theorem
- Sturmian Sequence
- Sturm-Liouville Equation
- Sturm-Liouville Theory
- Sturm Theorem
- Stäckel Determinant
- Stérmer Number
- Stöhr Sequence
- Subalgebra
- Subanalytic
- Subfactorial
- Subfield
- Subgraph
- Subgroup
- Sublime Number
- Submanifold
- Submatrix
- Subnormal
- Subordinate Norm
- Subscript
- Subsequence
- Subset