Lagrange's equation with one prime and three almost-primes

In this paper, we consider the representation of a large positive integer N≡4(mod24) in the form p2+x12+x22+x32 where p is a prime number and x1,x2,x3 are almost-primes. A positive integer is called a Pr-number if its number of prime factors counted according to multiplicity is at most r. We establish the above representation in the following two different forms.