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We intended to write this book simple and easy enough for those mathematics majors in their sophomore year or above while boiling down some of the contents to make it appropriate as a semester long number theory textbook without including quadratic congruences, sums of squares, and continued fractions. This book is not only suitable for those graduate students in mathematics as a number theory seminar reference who are not majoring in number theory, but also for those gifted juniors and seniors in high school as a guidance who are preparing for the International Mathematics Olympiad.