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Apr
28
reviewed Leave Open showing that $\Phi:\Pi_{1}(X,x_{0})\rightarrow [S^{1},X]$ is onto if $X$ is path connected.
Apr
28
comment Chinese Remainder theorem on Elliptic Curve group
But $3$ is not invertible in $\mathbb{Z}/15\mathbb{Z}$.
Apr
28
comment Chinese Remainder theorem on Elliptic Curve group
But $[0:2:3]$ is a projective point in $E(\mathbb{F}_5)$ and not equal to any of the affine points nor the identity. I'm not really sure what to make of the projective points to be honest. What would you do with the point $[0:0:3]$? Thanks for your input so far by the way.
Apr
28
comment Chinese Remainder theorem on Elliptic Curve group
I took it to be solutions to the following equation $y^2z=x^3+axz^2+bz^3\pmod{15}$ and not including $[0:0:0]$. "We define a natural group law on such curves ($E(\mathbb{Z}/N\mathbb{Z})$), although one usually gives these in terms of projective coordinates so as to cope with the occurrence of zero divisors."
Apr
28
revised Chinese Remainder theorem on Elliptic Curve group
added 152 characters in body
Apr
28
answered Chinese Remainder theorem on Elliptic Curve group
Apr
28
revised Chinese Remainder theorem on Elliptic Curve group
added 48 characters in body
Apr
28
comment Chinese Remainder theorem on Elliptic Curve group
Hey, thanks for your input. I've changed the question so that the curves are now non-singular. We have elliptic curves mod a composite number because this is looking at ECM, where we are factoring $N$. Lastly, I would think that $E$ should remain the same in some sense, else, it would look like one could choose the group then construct the curve and it'll be trivially true.
Apr
28
revised Chinese Remainder theorem on Elliptic Curve group
Changed $E$ to non-singular curves
Apr
28
asked Chinese Remainder theorem on Elliptic Curve group
Apr
25
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Apr
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reviewed Reject growth of the numbers $n$, such that $2n+1$ and $2n-1$ arent prime
Mar
31
reviewed Leave Open Finding the symmetry point in a quadratic graph
Mar
31
reviewed Close Find the general equation of g(x) where f(x)=0
Mar
31
reviewed Leave Open Efficient ways to read and learn a new topic
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31
reviewed Close Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
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31
reviewed Leave Open Is there a special term for an injection from A to B and a surjection from B to A.
Mar
31
reviewed Approve Question to understand how sections work
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31
reviewed Approve Find limit $\lim_{a\to 0} \, \frac{\left(a^{2 \varepsilon }-1\right) a^{x-\varepsilon }}{2 \varepsilon \log (a)}$
Mar
31
answered Proving that HK is a subgroup when K is normal