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Tignol, Jean-Pierre

Fields are number systems in which every linear equation
has a solution, such as the set of all rational
numbers $\mathbb{Q}$ or the set of all real numbers $\mathbb{R}$. 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.

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