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Values of integer polynomials
Polynomials are one of the most basic objects in mathematics - in particular, in number theory - yet the values they take remain largely mysterious! In number theory, one is generally interested in polynomials having integer or rational number coefficients, and the values they take at integral or rational arguments. In these three lectures, we examine three classical problems in number theory that involve understanding the values taken by integer polynomials, and give an overview of the long history of these problems and what is now known in each case.