Let p be a prime. For any diagonal quadratic form f, we define Qp(f) to be the set of integers represented by f with each variable of f is zero or not divisible by p. Then it seems to be interesting to determine the set Qp(f) when f is an universal diagonal quaternary quadratic form.

In this talk, we consider this problem for the case when f(x,y,z,w)=x2+y2+z2+5w2.