- geometry - ABCD is a parallelogram, P is any point on AC. Through P, MN . . .
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- Let $\\gcd(m,n)=d$. Show that if $a=b$ (mod $d$) the equations $x=a . . .
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- algebraic geometry - Why is a smooth connected scheme irreducible . . .
$\begingroup$ More generally, locally with finitely many irreducible components is enough (each point has a neighborhood with finitely many irreducible components)
- group theory - $a^ma^n=a^ {m+n}$ and $ (a^m)^n=a^ {mn}$ proof . . .
Here is a proof as I allude to in my comments, although this proof depends on having a more rigorous inductive definition of exponentiation as follows:
- quadratics - Newtons Identity - Mathematics Stack Exchange
While reading about quadratic equations, I came across Newton's Identity formula which said we can express $\alpha^n+\beta^n$ in simpler forms but not given any explanation
- Faster Distance formulae for higher n dimension
I need to calculate the distance two points, but these two points contain more than 100 dimensions With the regular two or three dimension distance formula, we can extend this further to n dimension
- How to simplify $a^n - b^n$? - Mathematics Stack Exchange
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- How to add and subtract values from an average?
Say I have 100 numbers that are averaged: number of values = 100 total sum of values = 2000 mean = 2000 100 = gt; 20 If I want to add a value and find out the new average: total sum of values =
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