Let F be an infinite field and let f(x), g(x)∈ F[x]. If f(a) = g(a) forinfinitely many elements a of F, show that f(x) = g(x).
Let F be an infinite field and let f(x), g(x)∈ F[x]. If f(a) = g(a) forinfinitely many elements a of F, show that f(x) = g(x).
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 10E
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Let F be an infinite field and let f(x), g(x)∈ F[x]. If f(a) = g(a) for
infinitely many elements a of F, show that f(x) = g(x).
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