How To Determine If A Large Number is Prime?
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How To Determine If A Large Number is Prime?

For a very large number n, how many divisibility tests are required to establish if its prime? I know this has something to do with the Golden Number, but...

Published: Aug 29, 2026

How does (sin2x)(cos2X) = (1/2)(sin4x)? [closed]
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How does (sin2x)(cos2X) = (1/2)(sin4x)? [closed]

I can't figure out how to simplify $\sin2\theta \cos2\theta$ to be $\frac12 \sin4\theta $. I assume double angle identities are involved, but I can&#...

Published: Aug 29, 2026

Questions about Trigonometry
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Questions about Trigonometry

I just learned the very basics of Trigonometry yesterday. I can answer all the questions on the homework but feel uneasy because I still have some questio...

Published: Aug 29, 2026

Combination with repetitions.
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Combination with repetitions.

The formula for computing a k-combination with repetitions from n elements is: $$\binom{n + k - 1}{k} = \binom{n + k - 1}{n - 1}$$ I would like if someone...

Published: Aug 29, 2026

Difference between
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Difference between "Show" and "Prove"

In many mathematics problems you see the phrase "prove that..." or "show that..." something is. What's the difference between these two phrases? Is "...

Published: Aug 29, 2026

The right way of proving LHS = RHS
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The right way of proving LHS = RHS

I'm currently brushing up on my math before heading back to school for my bachelor's and am practicing on some questions. Given the following eq...

Published: Aug 29, 2026

What does
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What does "with respect to x" mean when integrating?

When dealing with derivatives, "with respect to $x$" means we are observing how a small change in $x$ (the input) affects a change in $y$ (the o...

Published: Aug 29, 2026

How to find a normal vector on a surface from a point out of the surface?
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How to find a normal vector on a surface from a point out of the surface?

For example, if we consider a shape in 2D like a circle at center $(x_0,y_0)$ with radius R so the equation would be: $$f(x,y)=(x-x_0)^2+(y-y_0)^2-R^2$$ n...

Published: Aug 29, 2026

Find the least nonnegative residue
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Find the least nonnegative residue

Find the least nonnegative residue of $5^{18} \mod 11$. To do this I took $5^2 \equiv 3 \mod 11$. Then I did $(5^2)^5 \equiv 3^5 \mod 11$. And $3^5 \equiv...

Published: Aug 29, 2026

Determine whether the following statements are true or false, and then prove answers
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Determine whether the following statements are true or false, and then prove answers

Determine whether statement is true or false, and then prove answer. For all integers $a,b,c$: a) if $a|bc$ and gcd$(a,b) = 1$ then $a|c$ b) if $a|c$ and ...

Published: Aug 29, 2026

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