Let us fix a positive natural number $N$. When $i$ is a natural number smaller than $N$, coprime with $N$, we let $\mu(i)$ be the unique number in $\{1, \ldots, N1\}$ that is the multiplicative inverse of $Ni$ modulo $N$. I would like to know what is the maximum, when $i$ is in the range of the numbers from $1$ to $N1$ that are coprime with $N$, of the function $f(i):=i+\mu(i)$.
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