An extension of a theorem by Ljunggren
Michael A. Filaseta, Ikhalfani Solan · MATHEMATICA SCANDINAVICA · 1999
this paper are essentially the same as those of Ljunggren. He presented some key ideas introducing reciprocal polynomials into the problem of determining how polynomials with small Euclidean norm factor. The proof he gave of his theorem above involved consideration of several cases depending on the relative sizes of the exponents n, m, and p. In the case of Theorem 1 (or Theorem 2), we were able to bypass considering as many cases, mainly because the coefficients are more restrictive. We make no pretense here, however, of developing new approaches; this paper is merely a note that a five term version of Ljunggren's theorem does in fact exist. We give a proof of Theorem 1 below; a proof of Theorem 2 can be made with very few changes.