# A NOVEL CONCEPT OF THE BHATTACHARYYA’S THEOREM: √{-(x2+ y2)}= – √( x2+ y2 ) TO FIND THE SQUARE ROOT OF ANY NEGATIVE NUMBER INTRODUCING FERMAT’S LAST THEOREM IN REAL NUMBERS WITHOUT USING THE CONCEPT OF COMPLEX NUMBERS

#### Authors:

Prabir Chandra Bhattacharyya,

#### DOI NO:

https://doi.org/10.26782/jmcms.2024.05.00009

#### Keywords:

Extended form of Pythagoras Theorem,Fermat’s Last Theorem,Pythagoras Theorem,Rectangular Bhattacharyya’s Co-ordinate System,Theory of Dynamics of Numbers,

#### Abstract

In this paper, the author stated and proved Bhattacharyya’s Theorem: √{-(x2 + y2 )} = -√(x2 + y2). With the help of this theorem, the author finds the square root of any negative number introducing Fermat’s last theorem without using the concept of complex numbers. The author has introduced Fermat’s Last Theorem in Bhattacharyya’s Theorem to find the square root of any negative number in real numbers in a very simple way. Indeed it is a new invention in mathematics in this era.

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