Recent content by dpryor5

This makes intuitive sense to me. n divides into a*s with a remainder of 1, whereas a*x is divisible by n. It follows necessarily that x is divisible by n. But, it feels like this reasoning has to be explained more concretely for a good proof. I've been unable to do this by converting the...

as = 1 => a = 1/s ax = 0 => (1/s)x = 0 => x = 0.

Solving for a in the first equation, and substituting for it in the second. The closest I've been able to get to a system like that is using the equivalence of a ≡ b (mod n) to a mod n = b mod n. Applying that to the two congruence relations I start with produces: as mod n = 1 and ax mod n =...

Homework Statement Prove the following statement, or provide a counterexample showing its falsity: Let n be an integer greater than 1. For all a ∈ Z, if a is invertible mod n and there exists x ∈ Z such that ax ≡ 0 (mod n), then x ≡ 0 (mod n). Homework Equations If a is invertible mod n...