Primitive Roots

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• Primitive roots

  87356 Primitive Roots Determined Determine which elements of Z_7 (Z sub 7) are primitive roots.

• The Mobius Inversion Formula

  roots modulo p 2) Find all primitive roots modulo 5, modulo 9, modulo 11, modulo 13 and modulo 15.

• primitive root and its residue set

  This solution helps go through problems with regards to primitive roots and its residue set.

• Finding a Primitive Element of GF(49)

  Thus, neither of these roots are primitive either. Finally, the roots +/- 2i of x^2 + 4 also have multiplicative order 12, since the square of these roots is -4 = 3, which has multiplicative order 6 mod 7.

• Congruences, Primitive Roots, Indices and Table of Indices

  Congruences, Primitive Roots, Indices and Table of Indices are investigated. The solution is detailed and well presented.

• Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields.

  Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields

• the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields.

  Topics usually include the Euclidean algorithm, primes and unique factorization, congruences, Chinese Remainder Theorem, Hensel's Lemma, Diophantine equations, arithmetic in polynomial rings, primitive roots, quadratic reciprocity and quadratic fields

• Primitive polynomials and irreducible polynomials

  74839 Primitive polynomials 1) How do I show x+1 is primitive? 2) How do I prove x^4+x^3+1 is an irreducible polynomial of degree 4 over Z mod?

• Galois Theory : Use the method found in the proof below to find a primitive element for the extension Q(i, 5^(1/4)) over Q.

  Let , , then the minimum polynomial of is and it has two roots , ; the minimum polynomial of is and it has four roots , , , . Now we find some , such that , for . We can select and we get the element .