For integers modulo p, multiplication is modulo p-1. However, if you also include the roots of polynomials, multiplication is not modulo anything for all x there is an a=/=0 such that a^x=/=1.
So numbers mod p naturally produce the integers. There are more complicated processes going back the other way.
For integers modulo p, multiplication is modulo p-1. However, if you also include the roots of polynomials, multiplication is not modulo anything for all x there is an a=/=0 such that a^x=/=1.
So numbers mod p naturally produce the integers. There are more complicated processes going back the other way.