We consider the linear vector space formed by the elements of the finite field Fq with q = pr over Fp. Then the elements x of Fq have a unique representation in the form x = Σr j=1 cjaj with cj ∈ Fp; the coefficients cj will be called digits. Let D be a subset of Fp with 2 ≤ |D| < p. We consider elements x of Fq such that for their every digit cj we have cj ∈ D; then we say that the elements of Fp \ D are "missing digits". We will show that if D is a large enough subset of Fp, then there are squares with missing digits in Fq; if the degree of the polynomial f(x) ∈ Fq[X] is at least 2 then it assumes values with missing digits; there are generators g in Fq such that f(g) is of missing digits.
|Number of pages||10|
|Journal||Functiones et Approximatio, Commentarii Mathematici|
|Publication status||Published - júl. 1 2015|
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