  Necessary and sufficient conditions for the existence of an integer solution
of the diophantine equation $m/n=1/x(\lambda)+1/y(\lambda)+1/z(\lambda)$ with
$n=b+a\lambda$ are explicitly given for a,b coprime and a not a multiple of m .
The solution has the form $x(\lambda)=kn(\lambda)$,
$y(\lambda)=n(\lambda)(s+r\lambda)$, $z(\lambda)=(kl/r)(s+r\lambda)$ where
parameters $k,l,s,r\in \mathbb{Z}$ obey certain conditions depending on $a,b$.
The conditions imply restrictions for some choices of $a,b$ which differ from
the ones known in the case $m=4$. E.g., the modulus must be of the form
$l(mk-1)$. One can also deduce that primes of the form $1+4K$ are excluded as
modulus. Also if $a=p\ne m$ is prime and $b=a+1$, i.e., $n\equiv 1{\rm mod}\,
p$, polynomial solutions are shown to be impossible. All results are valid for
integers $m \ge 4$.
