Techniques of Solving Diophantine EQU'S Lead to Dio-Gandhi EQU'S. Mathematical Monographs

      Аннотация: Generally, we see the solutions with restricting in finite range; we use to find solutions for Diophantine equations. However, in my work, I have discussed and introduced a novel approach to solve Diophantine equations. Also, without restricting the solutions range and set (N or Z or Q or R or C), we can find solutions infinitely in some new Diophantine equations, which I call as, Dio-Gandhi equations. Precisely, we can find solutions in any range and in any set. I have an interest in several areas of mathematics, one of which is perhaps the oldest unsolved problem in mathematics, the existence (or otherwise) of an perfect number In 2008. I obtained a minor but original result, that any odd perfect number (if such exists) must have the form 12m + 1 or 324m + 81 or 468m + 117. In this thesis, we will establish some interesting and important theorems.

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