Abstract
Fields are number systems in which every linear equation
has a solution, such as the set of all rational
numbers Q or the set of all real numbers R. All fields
have the same properties in relation with systems of
linear equations, but quadratic equations behave differently
from field to field. Is there a field in which
every quadratic equation in five variables has a solution,
but some quadratic equation in four variables
has no solution? The answer is in this snapshot.