A Necessary and Sufficient Condition for k = ℚ 4 n 2 + 1 to Have Class Number ω n + c

Abstract

In this paper, we give a necessary and sufficient condition for real quadratic field k = ℚ 4 n 2 + 1 to have class number ω n + c where c ∈ 1 , 2 and ω n is the number of odd prime divisors of n .