An Attempt To Explore The Simple Alternate Second Solution To Fermat's Last Theorem, In Search Of Miraculous Proof, Is Presented Here …..

In the year of 1637 Pierre De Fermat an amateur French mathematician gave a famous note in the margin of the book of arithmetica of Diophantus of Alexandria , which his son published later, note in Latin is as follows :

“Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos & generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet”

which means in English as follows
“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. I have discovered a truly marvellous proof of this, which this margin is too narrow to contain.”
Mathematically it can be expressed as a,b,c,n all are integers n>2 an≠bn+cn This was originally conjectured in 1637.
The claimed Marvellous proof does not appear in any of the Fermat’s literature . But only one proof of n= 4 found in Fermat’s Literature .
Euler started epic journey for the proof , after one century of its conjecture , by solving the Theorem for number 3 . And in two centuries of its conjecture it was only solved for four numbers 3,4,5 and 7 . Proving it for all n>2 was a distant dream then . Up to 1980 it was solved for all n<400000. Theorem was finally proved in 1995 by Sir Andrew John wiles with his unparallel commitment and devotion by sacrificing seven years of his life for the cause of the proof.
It took four centuries to prove the Theorem for all n>2 .
A second alternative simple solution is presented here in search of miraculous proof.
An attempt is made here to prove it , from elementary mathematics
.
The alternative proof is simplified to the extent, that even a high school student, can understand the proof of Fermat's Last Theorem .
The journey of exploring the ocean of Mathematics is strange and amazing , it sometimes offers the sailor , precious gems, if he does not anchor his ships on the shore, and continue the journey of sailing his ship , in rough seas .

The truth arrived after extensive Mathematical Analysis is like recalling of our own forgotten memory of understanding of simple truth ….

The book is written with the hope that it will be helpful to, teachers and students of the subject of Mathematics, in understanding Fermat’s Last Theorem and its proof , as well as inspire teachers and students to admire, love and work on the subject of Mathematics.

In the year 2021 A Final conclusive proof was published with title “ LOST MIRACULOUS PROOF OF FERMAT’S LAST THEOREM” . In the present book proof of all earlier attempts is explained. In sort it is a transcript of journey to the final proof. All earlier tactics –methods devised were having some lacuna or shortfall- until it is finally concluded at last in the proof here described in chapter -13. Reader may omit all chapters from 3 to 12 ! . Once after reading chapter -13 to strengthen the understanding reader may read entire book. The concluding proof is mentioned in chapter 13 .