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After a careful study of some works of servaral authors on affine immersion of co-dimension one , co-dimension two , co-dimension three  and co-dimension four , we extend some of thier fundamental equations to affine immersion of genaral co-dimension p. Furthermore, we extend some theorem of Frank Dillen at el in  to affine immersion of general co-dimension and obtain the divisibility of the cubic forms by the second fundamental forms.
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