Consider the field with 16 elements constructed using the irreducible polynomial f(x) = 1 + x...

 

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Consider the field with 16 elements constructed using the irreducible polynomial f(x) = 1 + x³ + x4 over F₂. (i) Let a be a root of f(x). Show that a is a primitive element of F16. Represent each element both as a polynomial and as a power of a. Consider the field with 16 elements constructed using the irreducible polynomial f(x) = 1 + x³ + x4 over F₂. (i) Let a be a root of f(x). Show that a is a primitive element of F16. Represent each element both as a polynomial and as a power of a. Consider the field with 16 elements constructed using the irreducible polynomial f(x) = 1 + x³ + x4 over F₂. (i) Let a be a root of f(x). Show that a is a primitive element of F16. Represent each element both as a polynomial and as a power of a. Consider the field with 16 elements constructed using the irreducible polynomial f(x) = 1 + x³ + x4 over F₂. (i) Let a be a root of f(x). Show that a is a primitive element of F16. Represent each element both as a polynomial and as a power of a.

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To show that a is a primitive element of F16 we need to show that a generates all nonzero elements o... View the full answer