JP Journal of Algebra, Number Theory and Applications
Volume 37, Issue 1, Pages 21 - 30
(August 2015) http://dx.doi.org/10.17654/JPANTAAug2015_021_030 |
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NUMERIC PALINDROMES IN PRIMITIVE AND NON‑PRIMITIVE PYTHAGOREAN TRIPLES
John Rafael M. Antalan and Richard P. Tagle
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Abstract: In this paper, we consider numeric palindromes as components of a Pythagorean triple. We first show that there are infinitely many non-primitive Pythagorean triples that contain (i) a single numeric palindrome component, (ii) two numeric palindrome components and (iii) three numeric palindrome components. We then focus on numeric palindromes in primitive Pythagorean triples. We show that there are infinitely many primitive Pythagorean triples composed of a single and two numeric palindrome components. Open problem and preliminary results related to the open problem are also given. |
Keywords and phrases: Pythagorean equation, primitive Pythagorean triple, non-primitive Pythagorean triple, numeric palindrome, component. |
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