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We say that two polynomials f and g are equivalent over GF (p) if f(x) = g(x) for every x = GF (p). Select all true statements. f(x) = x¹0 and g(x) = x are equivalent under GF(11) f(x) = x¹¹ + 12x and g(x) = 2x are equivalent under GF (11) f(x) = x² and g(x) = 1 are equivalent under GF (5)

We say that two polynomials f and g are equivalent over GF (p) if f(x) = g(x) for every x = GF (p). Select all true statements. f(x) = x¹0 and g(x) = x are equivalent under GF(11) f(x) = x¹¹ + 12x and g(x) = 2x are equivalent under GF (11) f(x) = x² and g(x) = 1 are equivalent under GF (5)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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We say that two polynomials f and g are equivalent over GF (p) if f(x) = g(x) for every x = GF (p). Select all true statements. f(x) = x¹0 and g(x) = x are equivalent under GF(11) f(x) f(x) = x² and g(x) 1 are equivalent under GF (5) = = x¹¹ + 12x and g(x) = 2x are equivalent under GF (11) The minimum number of roots for a non-constant polynomial of even degree over the reals is 0. The minimum number of roots for a non-constant polynomial of even degree over GF (p) for any prime p is 0. The minimum number of roots for a non-constant polynomial of odd degree over the reals is 0. The minimum number of roots for a non-constant polynomial of odd degree over GF (p) for any prime p is 0.
Transcribed Image Text:We say that two polynomials f and g are equivalent over GF (p) if f(x) = g(x) for every x = GF (p). Select all true statements. f(x) = x¹0 and g(x) = x are equivalent under GF(11) f(x) f(x) = x² and g(x) 1 are equivalent under GF (5) = = x¹¹ + 12x and g(x) = 2x are equivalent under GF (11) The minimum number of roots for a non-constant polynomial of even degree over the reals is 0. The minimum number of roots for a non-constant polynomial of even degree over GF (p) for any prime p is 0. The minimum number of roots for a non-constant polynomial of odd degree over the reals is 0. The minimum number of roots for a non-constant polynomial of odd degree over GF (p) for any prime p is 0.
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