- Thread starter
- #1

#### hxthanh

##### New member

- Sep 20, 2013

- 16

**Number of solutions**

Le $n$ be a positive integer $(n\ge 6)$

How many triad $(a,b,c)$ are integers satisfying condition

$\begin{cases}a+b+c\equiv 0\pmod n\\ 1\le a<b<c\le n \end{cases}\quad$?

Result: $\left\lceil\dfrac{(n-1)(n-2)}{6}\right\rceil$

*note: $\lceil x\rceil$ is Ceilling Function (The least integer greater than or equal to $x$)

Last edited: