The aim of this book is to give the reader an oppurtunity to learn and to know interesting results in the elementary theory of numbers.Some aptitude is needed for general readers.Knowing is not enough and we should apply.Concentration is the powerful key that opens the door to accomplishment. We hope that students,researchers and anyone with an interest in numbers and equations may be motivated to search for new paths in solving system of multidegree multivariate polynomial diophantine equations."To succeed,we must first believe that we can.The more you can dream,the more you can do" as quoted by Michael Korda.It is worth to remember the remark observed by the Polish Mathematician Stefan Banach that "Mathematics is the most beautiful and most powerful creation of the human spirit"

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