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May
25
comment Order of prime ideals over split primes in the class group.
@James: You also have extra units if $d = -3$. But my point was to get you to see that the possibility that $a = 0$ exists. My example above is not unique to real quadratic fields; it works just as well with looking at $5$ in $\mathbf{Q}(\sqrt{-5})$.
May
25
comment Order of prime ideals over split primes in the class group.
@James: Why do you think that $a + b \sqrt{d} \sim a - b \sqrt{d}$ implies that $b = 0$? What is the unique (ramified) prime lying above $3$ in $\mathbf{Q}(\sqrt{3})$, for example?
May
24
comment Is there a classification of ideals of $\mathcal O_K$ ($K$ quadratic) over ramified and split primes depending on $d \pmod 4$?
You should look up Dedekind's criterion for splitting of primes, particularly as it relates to quadratic fields. This will tell you how to determine which primes are split, and to find generators for the primes lying over $p$.
May
20
revised How to find inverse of generator of a finite field?
edited tags
May
9
comment Determining whether a given algebraic number is an algebraic integer
The question was not to find a basis for $\mathcal{O}_K$, but to check whether a particular element is integral.
May
8
comment Characteristic of Quotient Ring
Consider $R = \mathbf{F}_p[x], I = (x)$. Both have characteristic $p$ and the quotient $R/I \simeq \mathbf{F}_p$ also has characteristic $p$.
May
1
reviewed Reject Let p be a prime. Consider the equation $\frac1x+\frac1y=\frac1p$. What are the solutions?
Apr
24
comment Most Common Difference Between Two Consecutive Primes?
Most occurring is not normally a useful notion when there are infinitely many elements in the list. As far as I know, it is not even known whether a positive proportion of prime gaps are bounded.
Apr
24
comment Most Common Difference Between Two Consecutive Primes?
Most common in what sense? Do you mean the average gap between primes?
Apr
24
comment Confusion between polynomial in field and factorization.
@Nancy: There is no requirement that the polynomials have degree less than $f$. Consider the prime factorization of a single prime integer $p$. It has only one factor appearing, exactly analogous to this situation.
Apr
24
revised Confusion between polynomial in field and factorization.
deleted 8 characters in body
Apr
24
reviewed Approve Confusion between polynomial in field and factorization.
Apr
19
reviewed Looks OK Factorising a cubic equation
Apr
19
reviewed No Action Needed A transfinite epistemic logic puzzle: what numbers did Cheryl give to Albert and Bernard?
Apr
19
comment Question about of the polynomial $x^p -x -a$
Exactly! (need more characters)
Apr
19
comment Question about of the polynomial $x^p -x -a$
Hint: If you have one root $\alpha$, can you find another (all of the other) root of $x^p-x-a$? The freshman's dream may be helpful here...
Apr
18
reviewed Leave Open a continuous function
Apr
18
reviewed Close Give a procedure using assignment statement to interchange the values of the variables $x$ and $y$.
Apr
18
reviewed Leave Open Find the sum of all odd numbers between two polynomials
Apr
18
reviewed Leave Open Identity in Ramanujan style