Nayuki Minase
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 Aug 27 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 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 25 comment Solve for $x$ in elliptic curve $y^2 = x^3 + ax + b$ Covering the secp256k1 case is sufficient for my purposes. 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. 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)? Apr 16 comment Prove that $\lfloor \lfloor x / a\rfloor / b \rfloor = \lfloor x / (ab) \rfloor$ @MathGems: I looked at your proof, but I'm not convinced about why those bi-implications are true. I found the proof by Brian M. Scott to be better explained and easier for me to understand. Apr 13 comment Prove that $\lfloor \lfloor x / a\rfloor / b \rfloor = \lfloor x / (ab) \rfloor$ Wow André, that was a pretty terse hint. But with some work, I was able to expand it into a full solution. Thanks! Apr 13 comment Prove that $\lfloor \lfloor x / a\rfloor / b \rfloor = \lfloor x / (ab) \rfloor$ You're right. Though I feel embarrassed about asking a duplicate question, I'd like thank you very much! Mar 3 comment Prove that if $2^n-1$ is prime, then $n$ divides $2^n-2$ I mean introduction of a new variable, whose role and meaning is unexplained. Mar 3 comment Prove that if $2^n-1$ is prime, then $n$ divides $2^n-2$ I am extremely uncomfortable with how much you left implied, such as the instantiation of $K$, the references to GCD, and the very non-obvious invocation of Fermat's little theorem for $K$. Only after rereading your proof a few times on separate days did I start to believe that it plausibly leads to an answer at all. -1. Mar 3 comment Prove that if $2^n-1$ is prime, then $n$ divides $2^n-2$ I didn't understand how your answer fits with my question. Please see the other answers as examples of proofs that I did understand. Mar 2 comment Prove that if $2^n-1$ is prime, then $n$ divides $2^n-2$ Other than that, I'm sorry but I don't understand your argument at all. Mar 2 comment Prove that if $2^n-1$ is prime, then $n$ divides $2^n-2$ Why are all your variables in uppercase? Feb 27 comment Prove that if $2^n-1$ is prime, then $n$ divides $2^n-2$ Alternate explanation: $p$ divides $2^n-1$, so $2^n-1$ divided by $p$ leaves no remainder, thus $2^n-1 \equiv 0 \mod p$. Feb 27 comment Prove that if $2^n-1$ is prime, then $n$ divides $2^n-2$ Ohh right, I understand now. I guess I'm not comfortable enough with modular arithmetic that such an elementary fact slipped past me, heh. Feb 27 comment Prove that if $2^n-1$ is prime, then $n$ divides $2^n-2$ You said "$p$ divides $2^n-1$, so $2^n \equiv 1 \pmod p$". How does this step work? Aug 11 comment Is there an everywhere discontinuous increasing function? I admit in full honesty that I asked this question out of curiosity; it is not a homework problem for me as my calculus course did not go this far. Aug 11 comment Is there an everywhere discontinuous increasing function? I should note for myself that $\lim_{x \rightarrow a^-} f(x)$ exists because of the least upper bound axiom for real numbers.