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For the positive integer $n$, let $f(n)$ denote the number of positiveinteger solutions $(n_1,\,n_2,\,n_3)$ of the Diophantine equation $$ {4\overn}={1\over n_1}+{1\over n_2}+{1\over n_3}. $$ For the prime number $p$, $f(p)$can be split into $f_1(p)+f_2(p),$ where $f_i(p)(i=1,\,2)$ counts thosesolutions with exactly $i$ of denominators$n_1,\,n_2,\,n_3$ divisible by $p.$  Recently Terence Tao proved that $$ \sum_{p< x}f_2(p)\ll x\log^2x\log\log x$$ with other results. But actually only the upper bound $x\log^2x\log\log^2x$can be obtained in his discussion. In this note we shall use an elementarymethod to save a factor $\log\log x$ and recover the above estimate.

A Note on Terence Tao's Paper "On the Number of Solutions to 4/p=1/n_1+1/n_2+1/n_3"