Determine all polynomials \( P(z) \) with integer coefficients such that, for any complex number \( z \) with \( |z| = 1 \), \( | P(z) | \leq 2 \).
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Tag Archives: integer coefficient
2013-08 Minimum of a set involving polynomials with integer coefficients
Let \( p \) be a prime number. Let \( S_p \) be the set of all positive integers \( n \) satisfying
\[
x^n – 1 = (x^p – x + 1) f(x) + p g(x)
\]
for some polynomials \( f \) and \( g \) with integer coefficients. Find all \( p \) for which \( p^p -1 \) is the minimum of \( S_p \).
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