منابع مشابه
Diophantine quadruples in Z [ √ − 2 ]
In this paper, we study the existence of Diophantine quadruples with the property D(z) in the ring Z[ √−2 ]. We find several new polynomial formulas for Diophantine quadruples with the property D(a+ b √−2 ), for integers a and b satisfying certain congruence conditions. These formulas, together with previous results on this subject by Abu Muriefah, Al-Rashed and Franušić, allow us to almost com...
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Philip Gibbs Diophantine m-tuples with property D(n), for n an integer, are sets of m positive integers such that the product of any two of them plus n is a square. Triples and quadruples with this property can be classed as regular or irregular according to whether they satisfy certain polynomial identities. Given any such m-tuple, a symmetric integer matrix can be formed with the elements of ...
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In this paper, we show that there does not exist a quadruple of positive integers a1 < a2 < a3 < a4 such that aiaj + 1 (i 6= j) are all members of the Tribonacci sequence (Tn)n≥0.
متن کاملDiophantine quadruples and Fibonacci numbers
A Diophantine m-tuple is a set of m positive integers with the property that product of any two of its distinct elements is one less then a square. In this survey we describe some problems and results concerning Diophantine m-tuples and their connections with Fibonacci numbers.
متن کاملSome polynomial formulas for Diophantine quadruples
The Greek mathematician Diophantus of Alexandria studied the following problem: Find four (positive rational) numbers such that the product of any two of them increased by 1 is a perfect square. He obtained the following solution: 1 16 , 33 16 , 17 4 , 105 16 (see [4]). Fermat obtained four positive integers satisfying the condition of the problem above: 1, 3, 8, 120. For example, 3 · 120+1 = 1...
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2015
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042115500475