I need some help with this problem: $$439^{233} \\mod 713$$ I can't calculate $439^{223}$ since it's a very big number, there must be a way to do this. Thanks.

Jul 10, 2021 · 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 ...

I can't seem to find a good way to solve this. I tried using L'Hopitals, but the derivative of log(n!) log (n!) is really ugly. I know that the answer is 1, but I do not know why the answer is one. …

Mar 25, 2016 · A friend of mine asked me how to derive the area and perimeter of a regular n n -gon with a radius r r for a design project he is working on. I came up with this, but I want to …

First, it may be helpful to factor out 2 2 from your series; it will only clutter up your actual work. So really, you are out for a formula of the nth n t h partial sum of ∑∞ n=0 1 3n ∑ n = 0 ∞ 1 3 n. As …

How to simplify an −bn a n b n? If it would be (a + b)n (a + b) n, then I could use the binomial theorem, but it's a bit different, and I have no idea how to solve it. Thanks in advance.

More generally, locally with finitely many irreducible components is enough (each point has a neighborhood with finitely many irreducible components). The full statement is then "every …

Feb 16, 2011 · I know that's an old thread but I had the same problem. I want to add a value to an existing average without having to calculate the total sum again. to add a value to an exisitng …

Dec 18, 2018 · Let B(X, Y) B (X, Y) be the family of all bounded maps from X X to Y, Y, normed linear maps. Then, B(X, Y) B (X, Y) is a Banach Space if Y Y is. Remark: I've seen this …

Apr 5, 2023 · I found this question talking about the relation between an equilateral triangle and cubics with three distinct real roots. Here's an image from the original post with an example: …