Open Internet by MindsNet

Rigorously proving the conjecture on n² divisibility of S(n)

The conjecture that n² divides the numerator of S(n) if and only if n is prime remains unproven. S(n) = Σ_{k=1..n} (2^k-2)/k. The challenge lies in rigorously handling Σ 2^k/k modulo p² and proving the converse for composite numbers.

Mathematics & logic, Mathematics, Number Theory