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comment How to solve equations to the fourth power?
Further reading: en.wikipedia.org/wiki/Rational_root_theorem
Aug
24
comment Show that the equation $y^2 = x^3 + 7$ has no integral solutions.
Note: This is the elliptic curve used in secp256k1, which has applications in computer cryptography.
Aug
24
revised Solve for $x$ in elliptic curve $y^2 = x^3 + ax + b$
added 59 characters in body
Aug
24
comment Solve for $x$ in elliptic curve $y^2 = x^3 + ax + b$
Thanks! I've implemented your algorithm and it works. Specifically I implemented $\rho$ and $x_1 = c^{(p+2)/9}$. I can see that for a random sample of $y$ values, only about 1/3 of them have any solution for $x$ at all. And of course when there's a solution, there are 3 solutions.
Jul
28
accepted Solve for $x$ in elliptic curve $y^2 = x^3 + ax + b$
Jul
25
revised Solve for $x$ in elliptic curve $y^2 = x^3 + ax + b$
added 12 characters in body
Jul
25
comment Solve for $x$ in elliptic curve $y^2 = x^3 + ax + b$
Covering the secp256k1 case is sufficient for my purposes.
Jul
25
asked Solve for $x$ in elliptic curve $y^2 = x^3 + ax + b$
Apr
23
awarded  Excavator
Apr
23
revised Confusing about logic gates
Domain name change
Apr
23
revised Good introductory books on primitive recursive functions
Domain name change
Apr
23
awarded  Teacher
Apr
23
suggested approved edit on Good introductory books on primitive recursive functions
Apr
23
answered Applying Fibonacci Fast Doubling Identities
Apr
23
suggested approved edit on Confusing about logic gates
Nov
7
awarded  Popular Question
Sep
28
awarded  Critic
Sep
28
comment How to write this in mathematical notation?
In your question, "either x or y" is misleading because it is possible for both x and y to be irrational and have their product be irrational too.
Sep
24
awarded  Popular Question
Apr
16
comment Prove that $\lfloor \lfloor x / a\rfloor / b \rfloor = \lfloor x / (ab) \rfloor$
(a) Is $k$ constrained to be an integer? (b) How does your proof address the fact that $m$ and $n$ must be positive integers (not arbitrary real numbers)?