The functional equation \(f(p+n^4+m^4)=g(p)+h(n^4)+h(m^4)\)

Abstract. The solutions \(f,g,h\) of the functional equation $$ f(p+n^4+m^4)=g(p)+h(n^4)+h(m^4) $$ are given under condition that every positive number of the form \(32640k\) is the difference of two primes.

Key words and phrases. Functional equation, reduced residue system, Dirichlet's theorem on arithmetic progressions.