A city-based retired professor has claimed to have given two solutions to Fermat's Last Theorem (FLT), the nearly 400-year old problem that has puzzled mathematicians the world over.
NAGPUR: A city-based retired professor has claimed to have given two solutions to Fermat's Last Theorem (FLT), the nearly 400-year old problem that has puzzled mathematicians the world over.
Prof V K Gurtu, the former Head of the Mathematics Department at the Laxminarayan Institute of Technology offered two solutions -- one based on the techniques prevalent during the 17th Century French judge and mathematician Pierre de Fermat's time and another using modern methods.
The 66-year-old professor presented the solutions to the mind-boggling 370-year-old problem at the International Congress of Mathematicians in Madrid, Spain last month, which was attended by leading lights from the world of math.
In his 28-page paper "On Fermat's Historic Marginal Note: Some Left Out Grains of Truth Leading to New Proof of FLT", Gurtu claims to have revealed facts which were left out by earliest researchers including Euler, Gauss, Dirichlet and Legendre who have proved the FLT to to the fifth power any number.
FLT has its origin in the Historic Marginal Note (HMN) Fermat (1601-1665) had written against the backdrop of Pythagoras Theorem in its arithmetic form in the book "Arithmetica" of Diophantus in 1637.
Fermat, in his margin note, claimed to have a solved the problem. However, no correct proof was found for 357 years until it was finally proven using very deep methods by Andrew Wiles in 1995 after a failed attempt a year before.
In the first proof, Gurtu uses identities known in Fermat's time and his well known method of infinite descent while in the second, non-natural numbers have been used for a very limited purpose.
Gurtu claims that his techniques are the closest to Fermat's thought process and has sent the paper to an American peer review journal for publication which is considering the solution.
"The first solution consists of a generalised form of representation of a number as a sum of two squares and Fermat's well known method of infinite descent," Gurtu said.
He said he had to introduce non-natural numbers of the form of square root for a limited purpose to prove the problem for odd prime numbers.
"The non-natural numbers eliminate themselves in the course of the solution of the equation without any difficulty," he said.
Gurtu said he pursued an investigative approach to the problem which was not based on the assumption that FLT had a solution.
The retired professor said he had been working on the problem since 1989 and had given a solution in 1998 to the Indian Mathematical Society, which had raised certain queries.
Gurtu claims to have found satisfactory answers to the queries in the last eight years.
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