H. Iwata, A property of some polynomials, Bull. Fac. Sci. Ibaraki Univ. Ser. A, No. 3 (1971), 21-24, (MR 54#6790).  Home/Search   Document Not in Database   Summary   Related Articles

....of prime divisors q for which f(x) splits completely modulo q. We recently learned the following Theorem 7 and its proof from Robert Gilmer who, in turn, learned it from Dennis Estes. But, after searching the literature, we discovered that the result dates back to a previous generation. Iwata [Iwat] gave simple proofs of Theorems 6 and 7 in 1971, and in his review of [Iwat] Gerst attributes both results to Frobenius [Fr2] THEOREM 7 (Frobenius) Suppose f(x) 2 ZZ[x] is an irreducible polynomial of degree d 2. Then f(x) fails to have a root modulo q for in nitely many primes q. PROOF. ....

....learned the following Theorem 7 and its proof from Robert Gilmer who, in turn, learned it from Dennis Estes. But, after searching the literature, we discovered that the result dates back to a previous generation. Iwata [Iwat] gave simple proofs of Theorems 6 and 7 in 1971, and in his review of [Iwat], Gerst attributes both results to Frobenius [Fr2] THEOREM 7 (Frobenius) Suppose f(x) 2 ZZ[x] is an irreducible polynomial of degree d 2. Then f(x) fails to have a root modulo q for in nitely many primes q. PROOF. The proof depends on the classical Frobenius Density Theorem. Suppose there ....

H. Iwata, A property of some polynomials, Bull. Fac. Sci. Ibaraki Univ. Ser. A, No. 3 (1971), 21-24, (MR 54#6790).

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