Pellian sequences and squares

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Journal Article
Notes on Intuitionistic Fuzzy Sets, 2012, 18 (4), pp. 7 - 10
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Elements of the Pell sequence satisfy a class of second order linear recurrence relations which interrelate a number of integer properties, such as elements of the rows of even and odd squares in the modular ring Z4. Integer Structure Analysis of this yields multiple-square equations exemplified by primitive Pythagorean triples, the Hoppenot equation and the equation for a sphere centred at the origin. The structure breaks down for higher powered triples so that solutions are blocked. However, Eulers extension of Fermats Last Theorem does not work as the structure does permit multiple power equations such as a 5 + b 5 + c 5 + d 5 = e 5
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