Question 128
a) Prove that for every natural number $n$ there exist natural $m$, $k$, that satisfy the equation
$$
k + m^k + n^{m^k} = 2009^n.
$$
b) Prove that there exist infinitely many natural $n$, for which such pair $m, k$ is unique.
$$
k + m^k + n^{m^k} = 2009^n.
$$
b) Prove that there exist infinitely many natural $n$, for which such pair $m, k$ is unique.