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Let us refresh our memories by remembering the well-known quotes of Gauss and Laplace, two of the greatest mathematicians of 18th-19th centuries, and take a vow to preserve the beauty of Arithmetic, the Queen of Mathematics, in terms of simplicity associated with the Indian ingenuity in expressing all the numbers by means of ten symbols only.

Mathematics, particularly the arithmetic of natural numbers, is not that though as it has been made out. This dictum of the author, having more than 45 years of teaching and research experience, holds good for research level problems also. But to experience this one has to go through this book entitled “FLT and some other outstanding number theory problems with their arithmetical solutions” wherein Goldbach conjecture and 3x+1 conjecture have also been proved by going into their genesis, while keeping intact their frame of reference. The solutions to most of such problems have to be simple but if they are getting tougher and complicated then there must be some problem with the approach adopted to solve it.
Though this book deals with research level problems but the approach adopted to solve them can also be easily understood by students and teachers at undergraduate level. In fact, it provides new path-breaking and thought-provoking research methodologies by which many more unsolved problems in number theory can be approached to arrive at their long-pending solutions.

Book Content of FLT

  1. Introduction
  2. Prime Numbers: mystery unfolded
  3. Arithmetic functions: some useful additions
  4. Representation of numbers as the sum of two squares
  5. Representation of numbers as the sum of more than two squares
  6. Representation of numbers in particular forms considered by Fermat
  7. Pythagorean Triples : Two new forms
  8. Fermat`s Last Theorem
  9. 3X + 1 conjecture
  10. Goldbach Conjecture
  11. Convergent and divergent sequences around golden ratios
  12. Fermat`s challenge-problem

Resolutions for ICM 2010
Distribution of Prime Numbers:
Analytic Formula sans Riemann Hypothesis




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Vishnu K. Gurtu


Himalaya pub