On reductibility of trinomials
Andrew Bremner · Glasgow Mathematical Journal · 1981
In Schinzel [1] the following interesting question is asked: does there exist an absolute constant K such that every trinomial in ℚ[x] has a factor irreducible in ℚ[x] which has at most K terms? The only known result appears to be that of Mrs. H. Smyczek, given in the above paper, that if K exists, then K ≥ 6. We here extend this bound to K ≥ 8 by exhibiting a trinomial in ℤ[x] which splits into the product of two irreducible factors, each having 8 terms.