Let p be an odd prime and suppose b is an integer whose order mod p = 7. Show that -b has order 14.
Here is where I am at:
I can rewrite then b^7 congruent to 1 mod p
Now, collary 7.2 in my book states order of a mod p divides p-1 .
So then 7|p-1. I am kind of stuck here...and I am looking for feedback on how to approach this using a valid theorem or proposition, because the one I am using is not going too well.