Note: A remark on a result of B. Segre concerning pseudoregular points of an elliptic quadric ofAG(2,q), q odd

In 1] S. ILKKA conjectured that pqeudoregular points of an elliptic quadric ofAG(2,q),q odd, only exist for small values ofq. In 3] B. SEGRE proves that an elliptic quadric ofAG(2,q),q odd, has pseudoregular points iffq=3 or 5. In 2], however, F. KáRTESZI shows that an elliptic quadric ofAG(2,7) has eight pseudoregular points. In this note we prove that part of B. Segre's proof is not correct, and that an elliptic quadric ofAG(2,q),q odd, has pseudoregular points iffq=3, 5 or 7.