p is a prime
$$
\sum_{a=1}^{p-1}\sum_{b=1}^{p-1}\frac{b}{a(ab)_p}=\frac{1}{2}p\ln^2 p+o(p\ln^2 p)
$$
$
(ab)_p\equiv ab(\mod p), 0<(ab)_p<p
$.
Is this equation true?Can anyone give a proof of it?
LMZ
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