1. State whether or not f(x) = 2x mod n is a bijection for all odd n and prove it 2. Relevant equations 3. The attempt at a solution So I'm pretty sure it is a bijection over testing it for some odd n, and the fact that gcd(2,n) = 1, thus there must exist an inverse for 2x mod n. However, I realize this proof makes no sense since I can make this argument for any function mod (a prime number) that it is a bijection, although not all functions mod prime are bijections. Any thoughts on where to go now?