### This question asks about using the Sage functionality for computing in Finite Fields.

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This question asks about using the Sage functionality for computing in Finite Fields.

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- Use Sage to create a finite field with 17 elements

In this field calculate:

The difference: 13 – 16

The sum: 11 + 10

The quotient: 1/2

The product: 3 * 8

The multiplicative inverse of: 5 - Use Sage to create a finite field with 32 elements. Let ‘a’ denote the primitive element.

In this field Calculate:

The difference: (a^2 + a) – (a + 1)

The multiplicative inverse of: a^4 + a + 1

The quotient (a^2 + 1)/(a^4 + a + 1) - Use Sage to create a finite field with 5^3 elements. Let ‘alpha’ denote the primitive element.

In this field Calculate:

The sum: (3*alpha^2 + 4*alpha) – (alpha^2 + 3)

The multiplicative inverse of: (alpha + 1)

The product: (alpha + 2)*(alpha + 3) - Use sage to create a finite field with 503,777,509 elements.

In this field calculate:

The quotient: 123,456,789/456,555,333

The multiplicative inverse of : 987,654,321

The difference: 789,123,456 – 444,333,111