Commentarii Mathematici Helvetici


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Volume 75, Issue 3, 2000, pp. 410–414
DOI: 10.1007/s000140050133

Universal octonary diagonal forms over some real quadratic fields

B. M. KIM[1]

(1) DEPARTMENT OF MATHEMATICS, COLLEGE OF NATURAL SCIENCE, KANGNUNG NATIONAL UNIV, 123 CHIBYON-DONG KANGNUNG, 210-702, KANGWON-DO, SOUTH KOREA

In this paper, we will prove there are infinitely many integers n such that n2 -- 1 is square-free and $ \Bbb Q(\sqrt {n^2-1}) $ admits universal octonary diagonal quadratic forms.

Keywords: Universal quadratic forms, real quadratic fields

KIM B. Universal octonary diagonal forms over some real quadratic fields. Comment. Math. Helv. 75 (2000), 410-414. doi: 10.1007/s000140050133