Smallest n for which 2^n-3 is Divisible by n

Theorem

The smallest positive integer $n$ such that $2^n - 3$ is divisible by $n$ is $4 \, 700 \, 063 \, 497$.

Proof

This theorem requires a proof. In particular: Brute force by the Lehmers, probably You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $4,679,307,774$

• 1994: Richard K. Guy: Unsolved Problems in Number Theory (2nd ed.): $\mathbf {A 10}$: Residues of powers of two.