Diophantine quadruples with the properties $$D(n_1)$$ and $$D(n_2)$$
نویسندگان
چکیده
منابع مشابه
Adjugates of Diophantine Quadruples
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 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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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: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
سال: 2019
ISSN: 1578-7303,1579-1505
DOI: 10.1007/s13398-019-00747-9