Proving that the integers mod p are a field

[wind crag]

I think I know how to prove the existence and uniqueness of the multiplicative inverse, but Im not sure how to do the other parts. It seems trivial to me, but I dont know if that's an acceptable answer on homework.

[dapper meteor]

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[storm kite]

Uniqueness is not actually required but follows from the field axioms (good exercise to prove)

but yeah, a+b mod p = a mod p + b mod p

And same for multiplication

So for a lot of the axioms, the proof follows from those facts and the fact that addition/multiplication of integers is associative/commutative/distributive

Which themselves are axioms unless you're taking a logic course or something

[wind crag]

Ah

Yeah that makes sense

Thanks

[storm kite]

np

[wind crag]

+close