Among four consecutive odd integers, one is divisible by 3. If one is divisible by 9, we get $3^2$, and if another is divisible by 3 (which happens in most cases), but since the step is 2, two of them can be divisible by 3 only if spaced by 6 — but only one in every three odd numbers is divisible by 3. So only one multiple of 3. So $3^1$ is guaranteed, $3^2$ is possible, but not guaranteed.

Sun, 03 May 2026 15:42:52 +0000

Understanding Odd Integers: The Mathematical Truth Behind Multiples of 3 and 9 Among four consecutive odd integers, a surprising pattern emerges rooted in divisibility by 3 and 9 — a fascinating insight that reveals the balance between distribution and structure in number sequences. When selecting four consecutive odd numbers (such as 5, 7, 9, 11 or 11, 13, 15, 17), a key observation is that exactly one of these numbers is divisible by 3. This arises because odd numbers increase by 2, and modulo 3, the odd residues cycle as 1, 0, 2 — ensuring only one step lands on a multiple of 3. Now, the condition states: If one of these numbers is divisible by 9 (i.e., 3²), alors nous obtenons un facteur $3^2$. Since divisibility by 9 implies divisibility by 3, we certainly get $3^1$ — and $3^2$ is possible but not guaranteed.