Sequences of [0,1]-polynomial with exponents in arithmetic progression

• Autores: Carrie E. Finch
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 110, Nº 1, 2012, págs. 75-81
• Idioma: inglés
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• Resumen

  • This paper finds the first irreducible polynomial in the sequence f1(x), f2(x),…, where fk(x)=1+∑ki=0xn+id, based on the values of n and d. In particular, when d and n are distinct, the author proves that if p is the smallest odd prime not dividing d−n, then fp−2(x) is irreducible, except in a few special cases. The author also completely characterizes the appearance of the first irreducible polynomial, if any, when d=n.