Algebra Math Help

Finite field generator – trying to remember some college algebra?

There is a theorem that if p is prime, then the lack of elements Z_p zero in a field, and furthermore, this field is cyclotomic. What is the main idea of the test? I sold my books on algebra, so they do not have easy access to the answer. How can I easily find a generator, for example, Z / (101Z) – all of the waste after dividing by 101? Sorry – I mean the multiplicative group of non-zero elements Mod (p). In this way, Z_p nonzero elements form a cyclic group under multiplication – the point of my question is to know the ideas that just this test. Thanks!

Any non-zero element has an inverse Z_p This can be Seeon this n Let 1=an+bp
so
an=1(mod p)
so n has an inverse mod p Cualquier campo finito, no sólo Z_p, tiene el grupo cíclico multiplicative. Here's a test: http://everything2.com/index.pl?node_id=672634

BLOSSOMS – The Broken Stick Experiment: Triangles, Random Numbers, and Probability