Problem Statement
Is every odd $n$ the sum of a squarefree number and a power of 2?
Categories:
Number Theory Additive Basis
Progress
Computational Verification
- Odlyzko: Verified up to $10^7$
- Hercher: Verified up to $\approx 1.12 \times 10^{15}$
Theoretical Connection
Granville and Soundararajan: If true, implies a positive proportion of primes are non-Wieferich primes.
Related
- Related: Problems #9, #10, #16
Source: erdosproblems.com/11 | Last verified: January 13, 2026