Prove it if it is true or give counterexample if it is false:
let a,b,k$\in$Z and n is positive integer, if a≡ b (mod n) then k^a ≡ k^b (mod n)
I think it is false statement like if -3≡ 2(mod 5) then 3^-3≢3^2(mod 5)
could you please check it for me ?
Your example is a good one, but it would be better to work out the calculation $3^2\equiv 4 \pmod 5$ and $3^{-3}=(3^3)^{-1}\equiv 2^{-1}\equiv 3 \pmod 5$ to show they disagree. The correct statement is Euler's theorem if $a \equiv b \pmod {\phi(n)}$ then $k^a \equiv k^b \pmod n$ where $\phi(n)$ is Euler's totient function.