1. Fermat's Little Theorem

Question 1

What is the order/period?
When does a have an order?

Answer 1

k such that a^k = 1 mod m
where m>1 and a c Zm

a has order in Zm if and only if a and m are coprime

Also a^t = 1mod m if t divides k

Question 2

linear congruence ; ax = b mod m

Answer 2

there exists an integer x if hcf (a,m) divides b