How to solve $x^2+x+1\equiv 0\pmod {11}$ ? I know that in some equations like $ax\equiv b\pmod d$ if $(a,d)=1$ then the equation has one and only one solu...

I'd like a hint toward how I could evaluate this definite integral. I'm aware it's likely to be non elementary and I haven't found a w...

I believe this should be a simple problem but I don't have an answer key to confirm if this is right, and some of the similar questions I can find on...

$f(x,y) = x^2+y^2-1$ $0=x^2+y^2-1 \Rightarrow y=\sqrt{1-x^2}$ I differentiaded $g(x)=\sqrt{1-x^2}$ with the chain rule and got $g'(x)=-\frac{x}{\sqrt...

I'm given the matrix exponential above and want to find $e^{-A}$. I was able to do so by simply making the negative exponents of the terms inside the...

Does the congruence $x^2 - 3x - 1 \equiv 0$ (mod 31957) have any solutions? (A hint given is that I can use the quadratic formula to find out what number ...

I have been applying the Gram-Schmidt procedure with great success however i am having difficulty in the next step, applying it to polynomials. Here i wha...

I have a hard time to find a way to construct a k-regular graph out of n vertices. There seems to be a lot of theoretical material on regular graphs on th...

Least integer principle: Every non-empty set of positive integers has a least element. Using this fact, define $r$ to be the least integer for which $j - ...

I am suppose to find $\sum_{n = 3}^\infty \frac{1}{n(n-1)}$ I am suppose to rewrite it as a telescoping series, but that isn't really defined so I do...