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using these axioms ( finite affine plane ) : AA1 : there exists at least 4...

using these axioms ( finite affine plane ) :

AA1 : there exists at least 4 distinct points , no there of which are collinear .

AA2 : there exists at least one line with n (n>1) points on it .

AA3 : Given two distinct points , there is exactly one line incident with both of them .

AA4 : Given a line l and a point p not on l , there is exactly one line through p that does not intersect l .

prove : in an affine plane of order n , each line l has exactly n-1 lines that do not intersect l .

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