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Fermat’s Last Theorem is proved using elementary arithmetic. Connection of this proof to Gӧdel’s Incompleteness Theorem is mentioned.
A proof of Fermat's last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity, symmetry, and transitivity), modus tollens, axiom of induction, the proof of Fermat's last theorem in the case of í µí±í µí± = 3 as well as the premises necessary for the formulation of the theorem itself. It involves a modification of Fermat's approach of infinite descent. The infinite descent is linked to induction starting from í µí±í µí± = 3 by modus tollens. An inductive series of modus tollens is constructed. The proof of the series by induction is equivalent to Fermat's last theorem. As far as Fermat had been proved the theorem for í µí±í µí± = 4, one can suggest that the proof for í µí±í µí± ≥ 4 was accessible to him.
The paper considers Fermat's theorem as a special case of the problem of least (smallest) deviation. It is proved that the theorem is true, since error can not vanish on the set of rational numbers.
The Bulletin of Symbolic Logic
What Does it Take to Prove Fermat's Last Theorem? Grothendieck and the Logic of Number Theory2010 •
This paper explores the set theoretic assumptions used in the current published proof of Fermat's Last Theorem, how these assumptions figure in the methods Wiles uses, and the currently known prospects for a proof using weaker assumptions.
English mathematics Professor, Sir Andrew John Wiles of the University of Cambridge finally and conclusively proved in 1995 Fermat's Last Theorem which had for 358 years notoriously resisted all gallant and spirited efforts to prove it even by three of the greatest mathematicians of all time -- such as Euler, Laplace and Gauss. Sir Professor Andrew Wiles's proof employs very advanced mathematical tools and methods that were not at all available in the known World during Fermat's days. Given that Fermat claimed to have had the `truly marvellous' proof, this fact that the proof only came after $358$ years of repeated failures by many notable mathematicians and that the proof came from mathematical tools and methods which are far ahead of Fermat's time, this has led many to doubt that Fermat actually did possess the `truly marvellous' proof which he claimed to have had. In this short reading, via elementary arithmetic methods, we demonstrate conclusively that Fermat's Last Theorem actually yields to our efforts to prove it. This proof is so elementary that anyone with a modicum of mathematical prowess in Fermat's days and in the intervening 358 years could have discovered this very proof. This brings us to the tentative conclusion that Fermat might very well have had the `truly marvellous' proof which he claimed to have had and his `truly marvellous' proof may very well have made use of elementary arithmetic methods.
2024 •
This book is about the famous mathematical conjecture knows as Fermat last theroem . Now this problem his been solved by a British mathematician Andrew Wiles and for this work he received 2016 Abel prize and the 2017 Copley medal.
English mathematics Professor, Sir Andrew John Wiles of the University of Cambridge finally and conclusively proved in 1995 Fermat's Last Theorem} which had for 358 years notoriously resisted all efforts to prove it. Sir Professor Andrew Wiles's proof employs very advanced mathematical tools and methods that were not at all available in the known World during Fermat's days. Given that Fermat claimed to have had the `truly marvellous' proof, this fact that the proof only came after 358 years of repeated failures by many notable mathematicians and that the proof came from mathematical tools and methods which are far ahead of Fermat's time, this has led many to doubt that Fermat actually did possess the `truly marvellous' proof which he claimed to have had. In this short reading, via elementary arithmetic methods which make use of Pythagoras theorem, we demonstrate conclusively that Fermat's Last Theorem actually yields to our efforts to prove it.
Reality instead of relativity
Reality instead of relativityThis article is critical to Einstein's two theories of relativity. Alternative interpretations to both theories are presented. These alternatives are based on classical physics concepts and without mysterious concepts, like dilation of time and bending of nothing.
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