A Diophantine problem with a prime and three squares of primes

We prove that if lambda(1), lambda(2), lambda(3) and lambda(4) are non-zero real numbers not all of the same sign, lambda(1)/lambda(2) is irrational, and pi is any real number then, for any epsilon > 0, the inequality vertical bar lambda(1)p(1) + lambda(2)p(2)(2) + lambda(3)p(3)(2) + lambda(4)p(4)(2) + pi vertical bar <= (max(j) p(j))(-1/18+epsilon) has infinitely many solutions in prime variables p(1), ..., p(4). (C) 2012 Elsevier Inc. All rights reserved.