Hopefully an easy question: the icosahedral group of order 60 (orientation preserving symmetries of a regular icosahedron) is isomorphic to the alternatin...

$$\log_{3x}81 = 2$$ How would I go about solving this? This is what I tried: $$\log_{3x}81 = 2$$ $$\frac{\log81}{\log 3 + \log x }= 2$$ Where do I go from...

In my textbook (Stewart's Calculus), the video tutor solutions for some problems use the squeeze theorem to determine the limit of a function. For ex...

We have two eigenvalues $\lambda_1$ and $\lambda_2$, with $\lambda_1 = \lambda_2 < 0$. Consider the case we have only one linearly independent eigenvec...

Suppose your RSA modulus is $55 = 5 * 11$ and your encryption exponent is $e = 3$. Find the decryption modulus d. I know $d = 40-13 = 27$ However, I get $...

Find a power series expansion of the function $f(x)=\dfrac1{1+x^7}$ about $x=0$. Use it to evaluate $\int_0^1 \dfrac1{1+x^7} dx$. Your answer should be ex...

I am searching for some groups, where it is not so obvious that they are groups. In the lecture's script there are only examples like $\mathbb{Z}$ un...

How many $10$-letter words can be formed using the $26$ letters of the alphabet if: a) Repetition is allowed b) Repetition is not allowed c) Repetition is...

Ball sort puzzle is that offline game, there is also another form of this game called water sort puzzle. In the game there are n stacks containing differe...

Converting an integer $N$ into binary and then reading the result as a base-10 number $N_2$, the prime $N=3$ gives $N_2=11$ (which is also prime) and $N=5...