arithmétique lycée recueilchapitre 5exercice 5.3pgcd
GCD computations
Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar · ★★★★★
Statement
- Soit $n$ un entier. Calculer $\mathrm{PGCD}(5n+2,\ 12n+5)$ et $\mathrm{PGCD}(9n+4,\ 2n-1)$.
- Soient $a$ et $b$ deux entiers non tous nuls. Supposons qu'ils existent trois entiers $c, x$ et $y$ tels que $c = ax + by$. Alors, on a : $\mathrm{PGCD}(a, b)$ divise $c$.
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Origin : Recueil COMIMa — Techniques de résolution de problèmes · 2026 · Madagascar
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