Pythagorean triples containing generalized Lucas numbers
نویسندگان
چکیده
منابع مشابه
ADDENDA TO "PYTHAGOREAN TRIPLES CONTAINING FIBONACCI NUMBERS: SOLUTIONS FOR Fn
then the Fibonacci numbers are given by Fn = Fn (1), and the Pell numbers are Pn = Fn(2). Cohn [4] has proved that the only perfect squares among the sequences {Fn(a)}9 a odd, are 0 and 1, and whenever a = k, a itself. Certain cases are known for a even [5]. The cited results of Cohn and Ljunggren mean that Conjectures 2.3,3.2, and 4.2 of [3] are true, and that the earlier results can be streng...
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Let n be a number. We say that n is square if and only if: (Def. 3) There exists m such that n = m2. Let us note that every number which is square is also natural. Let n be a natural number. Note that n2 is square. Let us observe that there exists a natural number which is even and square. Let us observe that there exists a natural number which is odd and square. Let us mention that there exist...
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The name comes from elementary geometry: if a right triangle has leg lengths x and y and hypotenuse length z, then x + y = z. Of course here x, y, z are positive real numbers. For most integer values of x and y, the integer x + y will not be a perfect square, so the positive real number √ x2 + y2 will be irrational: e.g. x = y = 1 =⇒ z = √ 2. However, a few integer solutions to x + y = z are fa...
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Petoukhov [1], [2], [3] has studied a family of bisymmetric 2 n x 2 n matrices that code the structure of the four DNA bases, the 64 codons that make up the 20 amino acids in all living structures, and beyond that, the proteins assembled from the amino acids as building blocks [1], [2], [3]. As the result of his studies he has found that the amino acids express certain degeneracies, 8 with high...
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A Pythagorean triple is a triple of positive integers a,b,c ∈ N+ satisfying a2 + b2 = c2. Is it true that, for any finite coloring of N+, at least one Pythagorean triple must be monochromatic? In other words, is the Diophantine equation X2 +Y 2 = Z2 regular? This problem has been open since several decades, even restricted to 2-colorings. In this note, we introduce partial morphisms, which are ...
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ژورنال
عنوان ژورنال: TURKISH JOURNAL OF MATHEMATICS
سال: 2018
ISSN: 1300-0098,1303-6149
DOI: 10.3906/mat-1702-102