1. The problem statement, all variables and given/known data Determine whether there is a positive integer k so that the congruence is satisfied. 2k ≡ 1 (mod 11) 2. Relevant equations gcd(2k,11) = 1 3. The attempt at a solution Well, I know the answer is false. Because of Fermat's Little Theorem, 2k ≡ 2 (mod 11) But I'm not satisfied with this answer. How could I show the answer to #1?