How Many Quadratic Forms Exist on Fp^n for an Odd Prime p?

alvielwj
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For an odd prime number p let Fp be the field with p elements, ie. the integers {0...,p-1} with addition and multiplication defined modulo p. How many quadratic forms are there on the vector space Fp^n

I don even know how to start this question
 
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are there infinite many quadratic forms on the vector space R^n ?
 
If F is any field with characteristic not 2, on Fn the quadratic forms are equivalent to the symmetric bilinear forms (essentially the symmetric n × n matrices over F).
 

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