On the size of Diophantine $m$-tuples for linear polynomials
نویسندگان
چکیده
منابع مشابه
Diophantine m-tuples for linear polynomials
In this paper, we prove that there does not exist a set with more than 26 polynomials with integer coefficients, such that the product of any two of them plus a linear polynomial is a square of a polynomial with integer coefficients. 1991 Mathematics Subject Classification: 11D09.
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Let n be a nonzero integer. A set of m 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 Diophantine m-tuple (with the property D(n)), or Pn-set of size m. Diophantus found the quadruple {1, 33, 68, 105} with the property D(256). The first Diophantine quadruple with the property D(1), the set {1...
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ژورنال
عنوان ژورنال: Miskolc Mathematical Notes
سال: 2017
ISSN: 1787-2405,1787-2413
DOI: 10.18514/mmn.2017.1533