Use Sage to create a finite field with 17 elementsIn this field calculate:The difference: 13 – 16The sum: 11 + 10The quotient: 1/2The product: 3 * 8The multiplicative inverse of: 5Use 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 + 1The 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: 123,456,789/456,555,333The multiplicative inverse of : 987,654,321The difference: 789,123,456 – 444,333,111

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