← All resources

arithmétique prépa recueilchapitre 1problème 1.3récurrence

A divisibility by 3^(n+1)

Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar ·

Statement

Montrez que $3^{n+1}$ divise $2^{3^n} + 1$ pour tout entier $n \geq 0$.

Preview rendered with KaTeX — the compiled PDF is the reference layout.

Source & credits

Origin : Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar

Reproduced for non-commercial educational purposes. Rights to the original statement belong to its authors / the competition organiser.

Downloads

PDFs are produced by the GitHub Actions pipeline: they may be missing in local development.

+ Add to problem set