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Some Results Connected with the Class Number Problem in Real Quadratic Fields

Authors:	Aleksander Grytczuk Jarosław Grytczuk

Institution:	(1) Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Gora, 65–516 Zielona Gora, Poland;(2) Institute of Mathematics, University of Zielona Góra, 65-516 ul. Szafrana 4a, Zielona Góra, Poland

Abstract:	We investigate arithmetic properties of certain subsets of square-free positive integers and obtain in this way some results concerning the class number h(d) of the real quadratic field $\mathbb{Q}{\left( {{\sqrt d }} \right)}$ . In particular, we give a new proof of the result of Hasse, asserting that in this case h(d) = 1 is possible only if d is of the form p, 2q or qr, where p, q, r are primes and q ≡ r ≡ 3(mod 4). Dedicated to Professor Włodzimierz Staś on the ocassion of his 80th birthday

Keywords:	The class number Real quadratic field
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