Diophantine quadruples with the properties D(n1) and D(n2)

• Autores: Andrej Dujella, Vinko Petričević
• Localización: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas ( RACSAM ), ISSN-e 1578-7303, Vol. 114, Nº. 1, 2020, págs. 448-456
• Idioma: inglés
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• Resumen

  • For a nonzero integer n, a set of m distinct nonzero integers {a1, a2,..., am} such that aia j +n is a perfect square for all 1 ≤ i < j ≤ m, is called a D(n)-m-tuple. In this paper, we show that there are infinitely many essentially different quadruples which are simultaneously D(n1)-quadruples and D(n2)-quadruples with n1 = n2.