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Abstract. We are concerned with the problem of minimizing the supremum norm on [0, 1] of a nonzero polynomial of degree at most n with integer coefficients. We use the structure of such polynomials to derive an efficient algorithm for computing them. We give a table of these polynomials for degree up to 75 and use a value from this table to answer an open problem due to P. Borwein and T. Erdélyi and improve a lower bound due to Flammang et al.

Some elementary results are given on restricted sums 2 ∧ A and 3 ∧ A of a subset A ⊂ Z/nZ, in the case when the cardinality of A is close to n/2. In the last section, some of these results are used to derive some new values of a function related to the Erdős-Ginzburg-Ziv problem.

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