On the number of divisors of x2 + x + A

Let A be a positive or negative rational integer such that integers in the field of √1 ? 4A have unique prime factorization. An elementary criterion will be obtained for x² + x + A to be a prime number, where x is a positive integer. The criterion implies that for positive A the polynomial x² + x + A is prime for x = 0, 1,…, A ? 2.