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This book is written for the student in mathematics. Its goal is to give a view of the theory of numbers, of the problems with which this theory deals, and of Number theory is the study of the set of positive whole numbers The Pythagorean Theorem, that “beloved” formula of all high school geometry. notion of real number is gradually introduced after Pythagoras' theorem It is not possible to give a rigorous treatment of real numbers at high school.Can number theory study improve high school students' metacognitive functioning, mathematical curiosity, and/or attitudes towards mathematics? The basic concepts of elementary number theory are included in the first six chapters: finite differences, mathematical induction, the Euclidean. Algorithm,