Frederic Nobbe

The Diophantine Equation 2^p - p = k^m: Closed Exponent Classes, a Uniform Exponent Bound, and Effective Finiteness

We study the equation 2^p − p = k^m in primes p and integers k, m ≥ 2. Exactly two solutions are known, (p,k,m) = (5,3,3) and (7,11,2), and an exhaustive computation reported here shows there are no others with p ≤ 10^6. Results. (A) The only solution with m even is (7,11,2); the...