Abstract
In this paper we will apply Biró's method in [A. Biró, Yokoi's conjecture, Acta Arith. 106 (2003) 85–104; A. Biró, Chowla's conjecture, Acta Arith. 107 (2003) 179–194] to class number 2 problem of real quadratic fields of Richaud–Degert type and will show that there are exactly 4 real quadratic fields of the form K = Q ( n 2 + 1 ) with class number 2, where n 2 + 1 is a even square free integer.
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