منابع مشابه
A Note on Diophantine Quintuples
Introduction. Diophantus noted that the rational numbers 1/16, 33/16, 17/4 and 105/16 have the following property: the product of any two of them increased by 1 is a square of a rational number (see [2, 3]). Let n be an integer. A set of positive integers {a1, a2, . . . , am} is said to have the property D(n) if aiaj + n is a perfect square for all 1 ≤ i < j ≤ m. Such a set is called a Diophant...
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A set {a1, . . . , am} of m distinct positive integers is called a Diophantine m-tuple if aiaj + 1 is a perfect square for all i, j with 1 ≤ i < j ≤ m. It is known that there does not exist a Diophantine sextuple and that there exist only finitely many Diophantine quintuples. In this paper, we first show that for a fixed Diophantine triple {a, b, c} with a < b < c, the number of Diophantine qui...
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متن کاملOn Diophantine quintuples and D(−1)-quadruples
In this paper the known upper bound 10 for the number of Diophantine quintuples is reduced to 6.8·10. The key ingredient for the improvement is that certain individual bounds on parameters are now combined with a more efficient counting of tuples, and estimated by sums over divisor functions. As a side effect, we also improve the known upper bound 4 ·10 for the number of D(−1)-quadruples to 5 ·...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1995
ISSN: 0025-5718
DOI: 10.2307/2153384