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Apr
24
comment Need help understanding Fibonacci Fast Doubling Proof
I see where you're coming from. There are some algorithms whose runtime is described in terms of the value instead of the bit length. For example: Ford-Fulkerson, subset sum (dynamic programming solution). But which convention to use is a matter of opinion and style, as long as the assumptions are stated clearly
Apr
24
comment Need help understanding Fibonacci Fast Doubling Proof
Your answer is largely excellent. I have a problem with the last paragraph - "exponential time to compute due to the size of the output". This is not true, because the bit length of the output is linearly proportional to the value of the input. In other words, $\log_2 F(n) \in O(n)$.
Mar
2
comment What does “adic” mean?
The third definition is also seen in programming, especially for variadic function
Mar
1
comment What's wrong with this transformation?
@tdudzik Among all your steps, not every step is a bi-implication. In particular, the second step is only valid if $\cos(x) \ne 0$.
Feb
23
comment Proving integer inequality
Awesome. Because in my world, buggy theorems can crash computer programs. =)
Feb
23
comment Proving integer inequality
A slight correction: The interval should be $(1, \infty)$ because $f(1)$ is a division by zero when $c=1$.
Feb
23
comment Proving integer inequality
Thanks! I was able to find more information based on the full name (which wasn't clear to me before). Bernoulli's inequality at Wikipedia
Feb
23
comment Proving integer inequality
How does the Bernoulli step work?
Feb
23
comment Proving integer inequality
If there happens to be an alternative simpler/shorter answer (such as one that involves manipulating integer inequalities without calculus), I would appreciate it. I want to fully understand and internalize this part of the proof before proceeding with work that builds on it.
Feb
23
comment Proving integer inequality
Thank you for the quick answer! I will incorporate it into my proof and verify each line before accepting. It looks reasonable and understandable to me at a glance.
Dec
28
comment What does E mean in 9.0122222900391E-5?
How does this page have 125K views now??
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!