  We study several related problems on polynomials with integer coefficients.
This includes the integer Chebyshev problem, and the Schur problems on means of
algebraic numbers. We also discuss interesting applications to approximation by
polynomials with integer coefficients, and to the growth of coefficients for
polynomials with roots located in prescribed sets. The distribution of zeros
for polynomials with integer coefficients plays an important role in all of
these problems.
