%0 Journal Article
%T Products of Odd Numbers or Prime Number Can Generate the Three Members¡¯ Families of Fermat Last Theorem and the Theorem Is Valid for Summation of Squares of More Than Two Natural Numbers
%A Susmita Pramanik
%A Deepak Kumar Das
%A Panchanan Pramanik
%J Advances in Pure Mathematics
%P 635-641
%@ 2160-0384
%D 2023
%I Scientific Research Publishing
%R 10.4236/apm.2023.1310043
%X Fermat¡¯s last theorem, had the statement that there are no natural numbers <em>A, B,</em> and <em>C</em> such that<em> A</em><em><sup>n</sup></em> + <em>B</em><em><sup>n</sup></em> = <em>C</em><em><sup>n</sup></em>, in which <em>n</em> is a natural number greater than 2. We have shown that any product of two odd numbers can generate Fermat or Pythagoras triple (<em>A, B, C</em>) following <em>n</em> = 2 and also it is applicable <em>A<sup>2</sup></em> + <em>B<sup>2</sup></em> + <em>C<sup>2</sup></em> + <em>D<sup>2</sup></em> + so on =<i>A<sub>n</sub><sup>2&nbsp;</sup></i>where all are natural numbers.
%K Fermat Last Theorem
%K Generation of Fermat¡¯s Numbers
%K Extension of Fermat¡¯s Expression
%K Fermat¡¯s Expression from Products of Odd Numbers
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=128210