Published January 20, 2019 | Version v1
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Generating Pythagorean Triples, Patterns, and Magic Squares

  • 1. Formarly, Professor of Mathematics, Federal University of Santa Catarina, Florianópolis, SC, Brazil


This  paper brings simplified and symmetric procedure to generate Pythagorean triples.  These triples are obtained in different procedures. First procedure is given in three blocks. The second procedure is the extension of first procedure, but in little different way. These triples are applied to generate perfect square sums magic squares of consecutive odd numbers, and  patterned Pythagorean triples. The patterned Pythagorean triples are obtained in two different way. One is a general way, and the second procedure give us Palindromic-Type Pandigital Pythagorean Triples in two different forms. As examples, the magic squares of orders 3 to 20 are given. The sum of entries of magic squares always give a perfect square resulting in a Pythagorean triple.



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