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Find number of elements in the set A_n(k)

Source: Romanian TST 1998

April 23, 2011
algebrapolynomialalgebra proposed

Problem Statement

Let nn be a positive integer and Pn\mathcal{P}_n be the set of integer polynomials of the form a0+a1x+…+anxna_0+a_1x+\ldots +a_nx^n where ∣ai∣≤2|a_i|\le 2 for i=0,1,…,ni=0,1,\ldots ,n. Find, for each positive integer kk, the number of elements of the set An(k)={f(k)∣f∈Pn}A_n(k)=\{f(k)|f\in \mathcal{P}_n \}.
Marian Andronache
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