Abstract
Given a commutative field K we define d(A,B):= (a1−b1)2−(a2−b2)2 for A=(a1,a2), B=(b1,b2) e K2. Given moreover a fixed k e KO, W. Benz has asked for all mappings σ: K2→K2 such that d(A,B)=k implies . This paper gives an answer if K=GF(p), p=5,7,11: σ must be a bijective collineation in case p = 7,11; there are non-injective mappings in case p=5. To obtain some of these results we have mads use of a computer.
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