A collection of equations satisfies the Hasse principle if, whenever one of the equations has solutions in and
all the , then the equations have solutions in the
Rationals . Examples include the set of equations

with , , and Integers, and the set of equations

for rational. The trivial solution is usually not taken into account when deciding if a collection of homogeneous equations satisfies the Hasse principle. The Hasse principle is sometimes called the Local-Global Principle.

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1999-05-25