# 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.
1. 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
2. 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)
3. 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)
4. 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

New York University
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