# Tagged Questions

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### Calculating powers

I was thinking how I could program powers into my application. And I want to do this without using the default math libraries. I want to use only +,-,* and /. So I wondered what is the definition of a ...
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### How to efficiently compute the coefficients in a bi-binomial expansion?

Is there a computationally efficient way of calculating the coefficients of the polynomial expansion of expressions like $(1+x^a)^m(1+x^b)^n$ for arbitrary positive integers $m,n,a,b$ (and especially ...
70 views

### taking the log of $a^b$ (Project Euler problem 29)

I've been stuck on Project Euler problem 29 and thus asked a friend who solved it how to do it. What he basically did was for each power was: $\left(\frac{\log_{10}(a)}{\log_{10}(2)}\right)\cdot b$ ...
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### Realistic Example of Power-Law Distribution?

I'm missing a bit of inbetween-math, and having some trouble understanding this, but: I want to generate a set of data that follows a power law. Let's say I have 10,000,000 people who like a ...
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### Formula to scale a series that is being bent with a root / power.

I have a reference number, Rx, and a series of numbers, Sx[], to compare to it. Let's call the output Ox[]. I am using a simple square root to accelerate the apparent difference between the reference ...
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### Does $\ (g^a Mod\ p)^b\,$ $\equiv$ $\ (g^a)^b (Mod\ p)\,$ hold true?

Are these two equations: $$\ (g^a Mod\ p)^b\,$$ $$\ (g^a)^b (Mod\ p)\,$$ one and the same? If yes then how And if no then how to solve the first equation?
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### Finding the value of $x$ for an equation

If we have the expression $a=x^{c\cdot x+1}$ where the values of $a,c$ are known, how can we find the value of $x$? I tried using log but it yields: $x = a ^ {(1/x)/(c-1/x)}$ from which I can't find ...
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### Power sums, fast algorithm

I know some schemes to compute power sums (I mean $1^k + 2^k + ... + n^k$) (here I assume that every integer multiplication can be done in $O(1)$ time for simplicity): one using just fast algorithm ...
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### Notation for Cartesian power, an oddity in the international standard

The Cartesian product of $A$ with itself $n$ times is normally denoted using superscript notation $A^n$, and this what ISO 31-11 defined as standard. However, ISO 31-11 has been superseded by ISO ...
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### What is the exact definition of a rational power?

I was taught in school that $$x^{a/b} = \sqrt[b]{x^a}$$ however, wolfram says this is not always true: $\sqrt[3]{x^2} \ne x^{2/3}$ ...
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### Are limits on exponents in moduli possible, if the modulus is relatively prime?

I asked a similar question to this recently. Here, I consider an arbitrary, but fixed, modulus m, which is relatively prime to x and y. Can anybody extend the answer given in the previous question? ...
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### Name of odd powered polynomial graph (Opposite of parabola(ic))

I am writing an assignment and have to describe the graphs for when the powers are even and when they are odd. I described the even power graphs as being parabolic or parabolas. The only problem is, I ...
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### What is the relationship between these expression?

Moderator Note: This is a Project Euler question If ...
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### Why does this general expression covering all f(u) reduce to a specific f(u)?

The following expression is sometimes encountered in statistical engineering and biology: $$r(u)=\frac{f(u)}{1-F(u)}$$ where $F(u)$ is the cumulative distribution function corresponding to the ...
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### Large powers of a banded and of a Toeplitz matrix

I would like to compute the p-th power of A, where A is a banded matrix. What is the best method to do that, if we suppose that p is large? In another case, where A is a Toeplitz matrix, which method ...
102 views

### How to find the last non-zero digit in ${^n\!P_k}$?

What is the procedure of finding the last non-zero element in ${^n\!P_k}$?
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### javascript “Property Tax” interest rate

I have an equation that calculates the Monthly Payment based on the Price, Down Payment, Term, and Interest Rate. Currently I am outputting a variable like so: ...
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### Is it true that $n> a^2\Rightarrow n!>a^n$, $n\in\mathbb{N}, a\in\mathbb{R}$?

If so, how can it be proven? (I have evaluated it up to $n=25$.) If not, does there exist a $k\in\mathbb{R}$ such as that $n> a^k\Rightarrow n!>a^n$, with $n\in\mathbb{N},a\in\mathbb{R}$? It ...