Let $n = 3m$ be an even integer and
$i = 1,2,\ldots, \lfloor\frac{n}{2}\rfloor$ $~~~$i.e.,$~~~$ $i = 1,2,\ldots, \frac{3m}{2} $.
I need to find the maximum value that $i$ can obtain from the set $S = \{1,2,\ldots, \lfloor\frac{n}{2}\rfloor\}$
if it is given that $i\equiv2(mod 3)$. Kindly help.
My attempt: When $3|\frac{3m}{2}$ then maximum value of $i$ is $\frac{3m}{2} -1$. Am I right for this particular part?
As $n$ is even, so is $m$, say $m=2k$. Then $\lfloor \frac n2\rfloor = 3k$. This is $\equiv 0\pmod 3$, but the second-laregst element of $S$, $ \frac n2-1$ is $\equiv 2\pmod 3$.