  Consider the congruence class R_m(a)={a+im:i\in Z} and the infinite
arithmetic progression P_m(a)={a+im:i\in N_0}. For positive integers a,b,c,d,m
the sum of products set R_m(a)R_m(b)+R_m(c)R_m(d) consists of all integers of
the form (a+im)(b+jm)+(c+km)(d+\ell m) for some i,j,k,\ell\in Z. It is proved
that if gcd(a,b,c,d,m)=1, then R_m(a)R_m(b)+R_m(c)R_m(d) is equal to the
congruence class R_m(ab+cd), and that the sum of products set
P_m(a)P_m(b)+P_m(c)P_m(d) eventually coincides with the infinite arithmetic
progression P_m(ab+cd).
