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Number theory, also known as higher arithmetic, is a branch of mathematics concerned with the properties of integers, rational numbers, irrational numbers, and real numbers. Sometimes the discipline is considered to include the imaginary and complex numbers as well. The main goal of number theory is to discover interesting and unexpected relationships between different sorts of numbers and to prove that these relationships are true. In this text we will describe a few typical number theoretic problems, some of which have known solutions too difficult for us to include, and some of which remain unsolved to this day.
