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Proof that $3^{105}+4^{105} \equiv 0 \;(\bmod\; 13)$
I'm trying to prove what he title says. I've found that (i'll type it that way for the sake of using less code i.e using $\vert$ instead of...
Apr 12, 2026
Archive: News
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What is Factorial of Zero Cubed?
My brother brought something to my attention earlier this morning and I cannot find the answer with just a googling to end the argument, so I have come to...
Apr 12, 2026
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Meaning of the word "conjugate" across mathematics?
Clearly, the word conjugate or conjugation is used for a myriad of different concepts across mathematics and even in science (see the Wikipedia page). Its...
Apr 12, 2026
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Does set $\mathbb{R}^+$ include zero?
I've been trying to find answer to this question for some time but in every document I've found so far it's taken for granted that reader k...
Apr 12, 2026
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What is the difference between the Taylor and Maclaurin series?
What is the difference between the Taylor and the Maclaurin series? Is the series representing sine the same both ways? Can someone describe an example fo...
Apr 12, 2026
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Topological Definition of Continuity
I am having some trouble understanding the mechanics of the topological definition of continuity. It has been defined as follows: A function $ f: \mathbb{...
Apr 12, 2026
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Hydrostatic Force on Triangle
A triangle with base 3 m and height 5 m is submerged vertically in water so that the tip is even with the surface. Express the hydrostatic force against o...
Apr 12, 2026
![How to calculate \sqrt{7+2\sqrt{10} } = [closed]](https://news.conceivablytech.com/uploads/how-to-calculate-sqrt-7-2-sqrt-10-closed_720.jpg)
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How to calculate \sqrt{7+2\sqrt{10} } = [closed]
$$ \sqrt[]{(\sqrt{7-2\sqrt[]{10}} + \sqrt[]{2})\cdot 2\sqrt[]{5}} $$ I know that the answer is $\sqrt[]{10}$, but how do I calculate it mathematically if ...
Apr 12, 2026
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Order of operations involving mod (%)
I was taking a programming test last night that had a math equation that simplified to 11 % 2 * 3, no () or likewise. When I compute it, being taught modu...
Apr 12, 2026
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Explaining the graph of $\sin(x^2) + \sin(y^2) = 1$
I had to plot the graph of the implicitly defined function $\sin^2 x + \sin^2 y = 1$ in an exam. This is not particularly difficult, but it got me wonderi...
Apr 12, 2026
