Primitive Pythagorean triples and generalized Fibonacci sequences

“Marin Drinov” Academic Publishing House of the Bulgarian Academy of Sciences
Publication Type:
Journal Article
Notes on Number Theory and Discrete Mathematics, 2017, 23 (1), pp. 54 - 62
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It is proved that infinite sequences of generalized Fibonacci sequences obtained from generalizations of the Golden Ratio can generate all primitive Pythagorean triples. This is a consequence of the integer structure since the major component of a primitive Pythagorean triple always has the form (4r1 + 1) where r1 belongs to the class in the modular ring Z4.
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