This pape; is concerned with distributional solutions of X1+…+ Xmd= U(X1+…+ Xm+n) where the X's are iid and independent ofUwhich takes values in [0,1]. WhenUis a constant the only possible non‐trivial solutions lie in the class of semi‐stable laws, and they are stable under a simple regularity condition. This material is reviewed. A unified account is given of some results known for the case whereUhas a beta (α, 1) law, apparently the only other case allowing explicit identification of all possible s