how to find mod 100 in the following case
what is the remainder when $3^{999}$ divided by 100? Is there is any short method to find remainder ? i tried $3^{1}$ divided by 100=3 $3^{2}$ divided by ...
20 Apr 2026 1 READS
Archive: News
Finding argument of complex number and conversion into polar form
How do I find the argument of a complex number, for example $z = 3 + 4i$? I know the polar form of $z$ is $r(\cos\theta + i\sin\theta)$ where $r$ is the m...
20 Apr 2026 1 READS
Relationship between Gaussian, Normal and Geodesic Curvatures
How do I show that the square of the gaussian curvature is the sum of the squares of the normal and geodesic curvatures other than the one shown in page 3...
20 Apr 2026 1 READS
Order of the Rubik's cube group
Associated to the Rubik's cube is a group as described in this Wikipedia article: $G = \langle F, B, U, L, D, R\rangle$. For example, the element $F$...
20 Apr 2026 1 READS
Finding rational canonical form for matrices
Consider the following matrices: $$A=\begin{bmatrix}2&-2&14 \\ 0&3&-7\\0&0&2\end{bmatrix} \text{ and } B=\begin{bmatrix}0&-4&a...
20 Apr 2026 1 READS
Existence of mixed-strategy Nash equilibrium
Consider the game below. Consider $p$ the probability of Player A playing U, and $(1-p)$ the probability of Player A playing D. Similarly, $q$ and $(1-q)$...
20 Apr 2026 1 READS
![Questions tagged [measure-theory]](https://edu.smbbmcl.edu.pk/uploads/questions-tagged-measure-theory_720.jpg)
Questions tagged [measure-theory]
Q&A for people studying math at any level and professionals in related fields
20 Apr 2026 1 READS
What is an intuitive definition of the zero vector?
I'm learning now about vector spaces and subspaces, and one of three rules that determine if something is a subspace of a larger vector space is that...
20 Apr 2026 1 READS
limit of quotient is quotient of limits
Prove the following: Let $X$ be a metric space. Let $E \subseteq X$. Let $p$ be a limit point of $E$, and let $f,g: E \subseteq X \to \mathbb{K}$ be a map...
20 Apr 2026 1 READS
Confusion about the null (empty) set being contained in other sets
I'm having a tough time understanding how the set theory of null sets work. I have: $$ X=\emptyset,\quad\quad Y = \{\emptyset\},\quad\quad Z = \{\{\e...
20 Apr 2026 1 READS
