For each of find necessary and sufficient conditions on such that there exists a tetrahedron with edges length and the remainder length .
%V0
For each of $k=1,2,3,4,5$ find necessary and sufficient conditions on $a>0$ such that there exists a tetrahedron with $k$ edges length $a$ and the remainder length $1$.
Izvor: Međunarodna matematička olimpijada, shortlist 1969
Školjka 
find necessary and sufficient conditions on 
such that there exists a tetrahedron with 
edges length 
and the remainder length 
.