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I have a couple of questions regarding the list of discriminants of real quadratic fields with narrow class number 1.

The sequence A003655 in OEIS portraits a list of discriminants of real quadratic fields with narrow class number 1. In the sequence there is no indication that the list is complete. Q1: Is that the case? Q2: In any case, could you point to some relevant references about this list?

Some afterthoughts and (further questions) after the first responses.

1. There are finitely many determinants $\Delta=4m>0$ with $m$ square-free and narrow class number 1. $\Delta=8$ is one such determinant, is it the only one? (references?).

2. If we have a determinant $\Delta=m>0$ with $m$ square-free and narrow class number 1, then $m$ is prime and congruent to 1 modulo 4.

Thanks in advance, and regards, Guillermo

I have a couple of questions regarding the list of discriminants of real quadratic fields with narrow class number 1.

The sequence A003655 in OEIS portraits a list of discriminants of real quadratic fields with narrow class number 1. In the sequence there is no indication that the list is complete. Q1: Is that the case? Q2: In any case, could you point to some relevant references about this list?

One further question following the first responses.

1. There are finitely many determinants $\Delta=4m>0$ with $m$ square-free and narrow class number 1. $\Delta=8$ is one such determinant, is it the only one? (references?).

Thanks in advance, and regards, Guillermo

I have a couple of questions regarding the list of discriminants of real quadratic fields with narrow class number 1.

The sequence A003655 in OEIS portraits a list of discriminants of real quadratic fields with narrow class number 1. In the sequence there is no indication that the list is complete. Q1: Is that the case? Q2: In any case, could you point to some relevant references about this list?

Some afterthoughts and (further questions) after the first responses.

1. There are finitely many determinants $\Delta=4m>0$ with $m$ square-free and narrow class number 1. $\Delta=8$ is one such determinant, is it the only one? (references?).

2. It is unknown whether or not there are infinitely many determinants $\Delta=m>0$ with $m$ square-free and narrow class number 1. So, Sequence A003655 only gives a few of them. (references for this conjecture?).

3. If we have a determinant $\Delta=m>0$ with $m$ square-free and narrow class number 1, then $m$ is prime and congruent to 1 modulo 4.

Thanks in advance, and regards, Guillermo

I have a couple of questions regarding the list of discriminants of real quadratic fields with narrow class number 1.

The sequence A003655 in OEIS portraits a list of discriminants of real quadratic fields with narrow class number 1. In the sequence there is no indication that the list is complete. Q1: Is that the case? Q2: In any case, could you point to some relevant references about this list?

Some afterthoughts and (further questions) after the first responses.

1. There are finitely many determinants $\Delta=4m>0$ with $m$ square-free and narrow class number 1. $\Delta=8$ is one such determinant, is it the only one? (references?).

2. If we have a determinant $\Delta=m>0$ with $m$ square-free and narrow class number 1, then $m$ is prime and congruent to 1 modulo 4.

Thanks in advance, and regards, Guillermo