Proof of a conjecture of Guy on class numbers
L Chua, B Gunby, S Park, A Yuan - International Journal of Number …, 2015 - World Scientific
L Chua, B Gunby, S Park, A Yuan
International Journal of Number Theory, 2015•World ScientificIt is well known that for any prime p≡ 3 (mod 4), the class numbers of the quadratic fields
and and h (-p), respectively, are odd. It is natural to ask whether there is a formula for h (p)/h
(-p) modulo powers of 2. We show the formula h (p)≡ h (-p) m (p)(mod 16), where m (p) is
an integer defined using the" negative" continued fraction expansion of. Our result solves a
conjecture of Richard Guy.
and and h (-p), respectively, are odd. It is natural to ask whether there is a formula for h (p)/h
(-p) modulo powers of 2. We show the formula h (p)≡ h (-p) m (p)(mod 16), where m (p) is
an integer defined using the" negative" continued fraction expansion of. Our result solves a
conjecture of Richard Guy.
It is well known that for any prime p ≡ 3 (mod 4), the class numbers of the quadratic fields and and h(-p), respectively, are odd. It is natural to ask whether there is a formula for h(p)/h(-p) modulo powers of 2. We show the formula h(p) ≡ h(-p)m(p) (mod 16), where m(p) is an integer defined using the "negative" continued fraction expansion of . Our result solves a conjecture of Richard Guy.
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