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2011•Journal of Science of the University of KelaniyaOpen access

A new interpretation of primitive Pythagorean triples and a conjecture related to Fermat's Last Theorem

R.A.D. Piyadasa, Jayantha Munasinghe, DK Mallawa Arachchi, K. H. C. H. Kumara

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Abstract

In this study primitive Pythagorean triples have been carefully examined and found that all of them satisfy a simple rule related to mean value theorem. It is pointed out that integral triples satisfying the equation on Fermat's Last Theorem should satisfy a special rule related to mean value theorem. A conjecture is proposed which may lead to find a simple proof of Fermat's Last Theorem. Keywords: Pythagorean triples; Fermat's Last Theorem DOI: 10.4038/josuk.v3i0.2742J. Sci. Univ. Kelaniya 3 (2007) : 93-98

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In this study primitive Pythagorean triples have been carefully examined and found that all of them satisfy a simple rule related to mean value theorem. It is pointed out that integral triples satisfying the equation on Fermat's Last Theorem should satisfy a special rule related to mean value theorem. A conjecture is proposed which may lead to find a simple proof of Fermat's Last Theorem. Keywords: Pythagorean triples; Fermat's Last Theorem DOI: 10.4038/josuk.v3i0.2742J. Sci. Univ. Kelaniya 3 (2007) : 93-98

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Available abstract

In this study primitive Pythagorean triples have been carefully examined and found that all of them satisfy a simple rule related to mean value theorem. It is pointed out that integral triples satisfying the equation on Fermat's Last Theorem should satisfy a special rule related to mean value theorem. A conjecture is proposed which may lead to find a simple proof of Fermat's Last Theorem. Keywords: Pythagorean triples; Fermat's Last Theorem DOI: 10.4038/josuk.v3i0.2742J. Sci. Univ. Kelaniya 3 (2007) : 93-98

Key concepts: Fermat's Last Theorem, Pythagorean theorem, Pythagorean triple, Mathematics, Fermat's little theorem, Wieferich prime, Proofs of Fermat's little theorem, Conjecture

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