BILINGUA in association with the Academy of Sciences of Abkhazia

R.A. Kamliya. Fermat’s Theorem: Another Proof. Monograph. “Apsny Sciences” series. – Sukhum-Moscow: BILINGUA, 2011.

This Monograph presents an elementary proof of Fermat’s theorem which is built upon certain properties of power residues.

For those interested in the theory of numbers.

"Apsny" is an ancient name of Abkhazia, a small Caucasian country where sciences have been paid much attention to.

This short monograph is the second book in the "Apsny Sciences" series.

Over four centuries ago Pierre de Fermat put forward his famous hypothesis: “It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers” [2]. Ever after many number theorists tried to prove the theorem, each suggesting his own way.

The approach by R.A. Kamliya demonstrated in this short publication is the result of a long research and thorough development. His previous study [1] unambiguously proved that the power residues modulo a prime can be unexpandable into a sum of two power residues. However, if at least one power residue is expandable, all the power residues are expandable modulo the selected number.

The present theory includes an essential preliminary theorem on expandability and the following original proof of Fermat’s theorem. The references are at the end of the book.

FERMAT`S THEOREM: ANOTHER PROOF