# All Questions

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### Calculating Newton Form of Interpolating Polynomial

For the function $f(x)=\frac{1}{x}$, I am trying to calculate the Newton form of the interpolating polynomial for the points $x_0=2$, $x_1=3$ and $x_2=4$. I understand that the Newton form of the ...
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### How does one evaluate $\lim_{n\to\infty}\int_0^x\frac{(x-t)^n}{(1-t)^{c+n+1}}dt$?

Where $c>0$ and $x\in\left[ 0,1\right)$
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### Proving divisibility of a large number

I need to prove that $2005\mid555\ldots 555$ there is the total of 800 digits. I've factorised $2005=5\times401$ and trivial reduced the problem to $401\mid 111 \ldots 111$. On every 200 digits there ...
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### Constructing a set with measure $\alpha$ on $[0,1]$ which is perfect and nowhere dense.

The answer is given as follows, I will type until the step where I think it is wrong, or this step might be insightful as to what I do not understand in the answer. Here is goes: The construction is ...
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### What is the Strategy in Computing Ideal Class Number?

I found many examples on computing ideal class numbers, but none gave an explicit statement on what we are examining when we are running through a list of elements with their norms written out. The ...
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### Integration of $\int_0^1 x\log\frac{1+x}{1-x} \, dx$

Wolfram Alpha gives $$\int_0^1 x\log \frac{1+x}{1-x}\,dx=1$$ I tried integration by part. But there is a convergence issue at $x=1$. Any help?
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### What is the degree of a prime ideal?

How is the degree of a prime ideal of an algebraic number field defined? An algebraic number field is a finite extension of $\mathbb{Q}$, right? A prime ideal is an ideal in a ring, i.e., a ...
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### Square of a differential

Just wondering, is this valid: $$\left(\frac{df}{dx}\right)^2=\frac{d^{2}f}{dx^{2}}$$