MODULAR ARITHMETIC 1. Introduction
... mod 4 is a refinement of congruence mod 2: even numbers are congruent to 0 or 2 mod 4 and odd numbers are congruent to 1 or 3 mod 4. For instance, 10 ≡ 2 mod 4 and 19 ≡ 3 mod 4. Congruence mod 4 is related to Master Locks. Every combination on a Master Lock is a triple of numbers (a, b, c) where a, ...
... mod 4 is a refinement of congruence mod 2: even numbers are congruent to 0 or 2 mod 4 and odd numbers are congruent to 1 or 3 mod 4. For instance, 10 ≡ 2 mod 4 and 19 ≡ 3 mod 4. Congruence mod 4 is related to Master Locks. Every combination on a Master Lock is a triple of numbers (a, b, c) where a, ...
GALOIS THEORY MICHAELMAS 2010 (M.W.F. 11AM, MR3
... polynomial ring Q[Ψ]. Then we require that Ψ7 − 6Ψ5 + Ψ4 + 3Ψ3 + Ψ − 13 = 0. This is done by passing to the quotient ring, under the equivalence relation defined by the ideal generated by Ψ7 − 6Ψ5 + Ψ4 + 3Ψ3 + Ψ − 13. Now you see the use of ring theory. And here the theorem that the ring of polynomia ...
... polynomial ring Q[Ψ]. Then we require that Ψ7 − 6Ψ5 + Ψ4 + 3Ψ3 + Ψ − 13 = 0. This is done by passing to the quotient ring, under the equivalence relation defined by the ideal generated by Ψ7 − 6Ψ5 + Ψ4 + 3Ψ3 + Ψ − 13. Now you see the use of ring theory. And here the theorem that the ring of polynomia ...
