How do you prove the multiplicative integers (mod p) has at least one generator?
I know how to show a^(p-1) is congruent to 1 using Fermat's Little Theorem but how do you show p-1 is the smallest such integer?
Thanks!
How do you prove the multiplicative integers (mod p) has at least one generator?
I know how to show a^(p-1) is congruent to 1 using Fermat's Little Theorem but how do you show p-1 is the smallest such integer?
Thanks!
What I mean is how do I show that there is at least one integer whose smallest power that makes it congruent to 1 must be p-1?
In other words prove that the group of multiplicative integers (mod p) where p is prime must have at least one generator.
...as you say other (non-generator) integers have smaller powers that make them congruent to 1.