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Research Paper | Earth Science and Engineering | India | Volume 10 Issue 2, February 2021

Innovating Extension of Almost Pythagorean Triples in Prime Numbers and Possible Uses in Science

Somnath Mahapatra

Abstract: A Pythagorean triple (PT) consists of three natural numbers a, b, and c, which follow the mathematical relation: a*a + b*b = c*c, and is commonly written as (a, b, c). Pythagorean triples are useful in various fields of Science and Technology, especially in Mathematics. In recent past, some new triples (x, y, z) of 3 natural numbers were found to follow the mathematical relation: x*x + y*y = z*z+1, (very close to the PT relation), and have been given the name Almost Pythagorean Triples (APTs). I have found several Almost Pythagorean Triples in prime numbers and in my present work, I have shown that their relation has very small percentage of deviation (PD %) from PT relation. It has been shown that multiples of an APT (MAPTs) show same amount of percentage of deviation (from PT relation) as the corresponding APT. APTs and MAPTs can have several uses and applications in Mathematics and other fields of Science & Technology.

Keywords: Pythagorean triple, Almost Pythagorean Triples, prime numbers, percentage of deviation

Edition: Volume 10 Issue 2, February 2021,

Pages: 1230 - 1234