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A set $\{a_1, a_2, \cdots, a_m\}$ of $m$ distinct positive integers is called a $D(-1)$-$m$-tuple if the product of any distinct two elements in the set decreased by one is a perfect square. In this paper, we find a solution of Pellian equations which is constructed by $D(-1)$-triples and using this result, we prove the extendibility of $D(-1)$-pair with some conditions.
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참고문헌 (13)
참고문헌 신청
A. Baker / 1993 / Logarithmic forms and group varieties / J. Reine Angew. Math 442:19~62
E. Brown / 1985 / Sets in which xy + k is always a square / Math. Comp 45:613~620
L. E. Dickson / 1966 / History of the Theory of Numbers Vol.2 / Chelsea
A. Dujella / 1998 / Complete solution of a family of simultaneous Pellian equations / Acta Math. Inform. Univ. Ostraviensis 6(1):59~67
A. Dujella / 2000 / A parametric family of elliptic curves / Acta Arith 94(1):87~101
E. Brown / 1985 / Sets in which xy + k is always a square / Math. Comp 45:613~620
L. E. Dickson / 1966 / History of the Theory of Numbers Vol.2 / Chelsea
A. Dujella / 1998 / Complete solution of a family of simultaneous Pellian equations / Acta Math. Inform. Univ. Ostraviensis 6(1):59~67
A. Dujella / 2000 / A parametric family of elliptic curves / Acta Arith 94(1):87~101
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