arithmétique lycée recueilchapitre 5problème 5.1congruences
A sum of powers
Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar · ★★★★★
Statement
Soit $A = 3^{105} + 4^{105}$. Montrer que $7$ divise $A$. Calculer $A \pmod{11}$ et $A \pmod{13}$.
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 Was this exercise useful?