I will need to know the Well Ordering Axiom, The Division Algorithm, Euclidean Algorithm, The Fundamental Theorem of Arithmetic, the theorem which says that the gcd of is the smallest positive integer that can be written as a linear combination of two integers and maybe their proofs (?). And I will need to be able to use all other theorems to work problems or write proofs.
Also I will need to know the definitions of mods, concruence classes, rings, commutative rings with or without identity, integral domains, fields, subfields, units, zero divisors, isomorphisms, homomorphisms, bijective functions, and properties of the integers mod a prime number.
I think I got it all...I'll find out tomorrow.
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