Basic step Show that $P(2)$ is true: $$2! < (2)^2$$ $$1*2 < 2*2$$ $$2 < 4 \quad \text{(which is true)}$$ Inductive Step Assume $P(k) \implies (k)...

For reference: (Exact copy of the problem) In the right triangle, right angle in $B$; $I$ is incenter and $E$ is excenter for $BC$.If $AI = IE$, calculate...

I have taken an interest in this topic recently. If one is unfamiliar with matroids, I will give the definition here. Let $M=(E,\mathcal I)$ where $E$ is ...

Consider a grammar for calculator language. This language consists of all arithmetic expressions that can be evaluated by a calculator, i.e. expressions o...

Both gradient and total derivative are a collection or combination of the partial derivatives with respect to each input variable?

A few years ago, the Boolean Pythagorean Triples problem was solved and shown to be impossible for $n\ge 7825$. Is there a way to show that the number $n$...

I'm given the equation $ 2x \equiv 5\pmod 9 $ and am told to solve for the linear congruence. I attempted this with only the methods taught to me and...

The ellipses is where I'm stuck. I don't think a simple algebraic manipulation will work here.

Is the circumcenter of an equilateral triangle equidistant from its 3 vertices? If yes, how can I prove that?

I am trying to find a linear factorization of the polynomial $$p(z) = 1 +z+z^2 +z^3 +z^4 +z^5 + z^6 +z^7 +z^8$$ I know what it means by linear factorizati...