> You may consult the following paper by Christian Elsholtz & Terence Tao: https://terrytao.wordpress.com/tag/erdos-straus-conjecture/ A natural solution $\ (p\ x\ y\ z)\ $ of Erdös-Straus equation $$ \frac 4p = \frac 1x+\frac 1y+\frac 1z $$ is of ET-type $I$ if $\ x\ $, but not $\ y\ $ nor $\ z,\ $ is divisible by $\ p\ $. A natural solution $\ (p\ x\ y\ z)\ $ of the same Erdös-Straus equation is of ET-type $II$ if both $y$ and $z$, but not $x$, are divisible by $p$ >Are the ET-type $I$ solutions superfluos? -- i.e. <hr /> **QUESTION**: Is every prime $p$ represented by an ET-type $I$ solution also represented by an ET-type $II$ as well? <hr />