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.