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Number of solutions a + b + c ≡ 0 (mod n)

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 $x$)
 
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