Q. Which of the following are irreducible polynomials?

i) X^4+X^3
ii) 1
iii) X^2+1
iv) X^4+X+1

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Q. The polynomial f(x)=x^3+x+1 is a reducible.

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Q. 5/3 mod 7 =

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Q. -5 mod -3 =

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Q. Multiply 00100110 by 10011110 in GF(2^8) with modulus 100011011.The result is

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Q. Find the inverse of (x^7+x+1) modulo (x^8 + x^4 + x^3+ x + 1).

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Q. 7x = 6 mod 5. Then the value of x is

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Q. State whether the following statement is true or false over a field.

The product of monic polynomials is monic.

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Q. State whether the following statement is true or false over a field.

The product of polynomials of degrees m and n has a degree m+n+1.

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Q. State whether the following statement is true or false over a field.

The sum of polynomials of degrees m and n has degree max[m,n].

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Q. Is x^3 + 1 reducible over GF(2)

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Q. Is x^3 + x^2 + 1 reducible over GF(2)

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Q. Is x^4 + 1 reducible over GF(2)

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Q. The result of (x2 ⊗ P), and the result of (x ⊗ (x ⊗ P)) are the same, where P is a polynomial.

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Q. Find the 8-bit word related to the polynomial x^6 + x + 1

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Q. “An Equations has either no solution or exactly three incongruent solutions”

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Q. Find the solution of x^2 ≡ 3 mod 11

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Q. Find the solution of x^2 ≡ 2 mod 11

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Q. Find the set of quadratic residues in the set –

Z11* = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

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Q. In Zp* with (p-1) elements exactly:

(p – 1)/2 elements are QR and
(p – 1)/2 elements are QNR.

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