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Feb
5
comment Combinatorics - pigeonhole principle question
Looks fine to me.
Feb
4
comment Solution of a system with exponentials
Smarter than subtracting $1$ from both sides and taking logs?
Feb
4
comment Optimization Puzzle
@Ross, yes, the interesting question is which GCDs to build when you have several targets.
Feb
3
comment Optimization Puzzle
So you have a directed graph with vertices corresponding to $\mathbb{Z}^+$ and edges $n \to kn$ with weight $k$ for all $n, k$. The task is to find the connected subgraph containing $1$ and the specified targets which has least total weight. As an optimisation, I think Patrick87's answer shows that you only need consider prime values of $k$.
Feb
2
comment How to compute Shannon information?
@Yrogirg, if you define "good" tightly enough and have a sufficiently precise value of $H_n$ then you might be able to recover the frequencies and calculate the true probabilities; otherwise, don't expect much joy.
Feb
2
comment How to solve quadratic over square root of quartic equals constant?
Can't you square and rearrange to a quartic, solve the quartic with Sturm sequences and Newton's method, and then check the solutions against the original equation?
Jan
31
comment Perfect Squares ending in 576
It doesn't have to be circular. $1000 | (n^2 + 48n)$, so substitute $n = 4m$ and get $125 | \left(m(m + 12)\right)$, whence either $125|m$ or $125|(m+12)$. That's enough to start generating much shorter lists of candidates.
Jan
30
comment Let $\psi$ be a wavelet. Can its Fourier transform $\hat{\psi}$ be also wavelet?
In fact this is part of a family of wavelets, the Gabor wavelets, which is closed under Fourier transform.
Jan
30
comment Direct proof that $\pi$ is not constructible
Sure, but you were asking for a direct proof. That seems fairly indirect.
Jan
30
comment Direct proof that $\pi$ is not constructible
Maybe I'm missing something, but doesn't squaring the circle construct $\sqrt{\pi}$?
Jan
29
comment Why is integer factorization considered to be in NP if a quantum computer can compute a factorization in polynomial time?
Do you have a reference for integer factorisation being considered to not be in P? I don't believe that many people have strong beliefs either way.
Jan
29
comment What does the Fourier Transform mean in the context of images?
What part are you having difficulty understanding? An image as a function? 2D Fourier transform? Something else?
Jan
24
comment Converting polynomials to depressed form
Yes, it can. ${}{}$
Jan
20
comment Can this primality test be optimized to runs in polynomial time?
Given how long it took to prove that primality testing was in P, and how much more complicated AKS primality testing is than this, I highly doubt it.
Jan
20
comment Can this primality test be optimized to runs in polynomial time?
But that doesn't help, because performing $O(1)$ work for each of $\sqrt{n}$ candidates is already exponential time, as $\sqrt{n}$ is exponential in $\log(n)$, which is the input size.
Jan
18
comment How to express $2012$ in terms of three consecutive primes?
There's no need to check so many cases. You just need to consider the consecutive primes 41, 43, 47, 53. 41*47=1927 is far too small, 43*53=2279 is far too large, and while 43*47=2021 is quite close, 9 is neither 41 nor 53.
Jan
18
comment How to express $2012$ in terms of three consecutive primes?
@pedja, $+$ is a function.
Jan
18
comment How to express $2012$ in terms of three consecutive primes?
What operations are elementary? $$\lfloor\sqrt[(4048243-4048241)]{4048229}\rfloor$$ presumably doesn't count?
Jan
18
comment Set of all points which are a specified angle away from a given point on a sphere.
To clarify: you want to parameterise the intersection of the sphere with a plane (taking as an assumption that they intersect)?
Jan
17
comment Evaluate this finite summation
Have you tried using Gosper's algorithm or (since it has compact support) Zeilberger's algorithm?