In Bertrand Russell and Alfred Whitehead’s Principia Mathematica, they note that “The proofs of *2.37.38 are exactly analogous to that of *2.36.” I have found a proof of *2.37, but would like to know a proof of *2.38, using the same format. My proof of *2.37: $$Dem. $$ $$ [Perm \frac{q,p}{p,q}] \vdash:q \vee p.\supset.p\vee q […]

# Tag: Q

$p\cdot q\cdot r=a^3-1+43\cdot (b^2-1)$ p, q, r are primes. a, b integers>0. Is this equation a Mordell equation? Has this equation infinitely many solutions?

Here’s the part of the code var Ctx = context.Background() DSClient, err := datastore.NewClient(Ctx, PROJECT_ID) if err != nil { log.Fatal(“Couldn’t connect to DataStore: “, err) } log.Print(“DataStore Client: “, DSClient) q := datastore.NewQuery(“users”).Filter(“email=”, greq.Email).Limit(1) keys, err := config.DSClient.GetAll(config.Ctx, q, &urs) I’m getting following error. http: panic serving 127.0.0.1:60844: runtime error: invalid memory address or […]

I am curious to know if there are infinitely many primes $p$, $q$, $r$ such that $p\cdot q\cdot r\equiv a^3-1\pmod {(b^3+1)}$, for $p$, $q$, $r$, $a$, $b$ coprime and $a, b>0$, with $a^3-1, b^3+1 < p\cdot q\cdot r$.

Triangle $ABC$ is given with $|AB|=3$, $|AC|=7$ and $|BC|=8$. Points $P$, $Q$, and $T$ are chosen on the sides $|AB|$, $|AC|$ and $|BC|$ of triangle $ABC$, respectively. It is given that $|AP|=|AQ|=1$, $|BP|=|BT|=2$ and $|CQ|=|CT|=6$. Find the measure of angle $<PQT$. I have solved this easily using cosine rule and the answer is 60 degrees. […]

Really basic simple stuff. I would like to be able to assign “a”, “b”, and “c” values to do basic math on Gnome Calculator but I get a “malformed expression” error when trying to assign “b” or “c”. I tried using uppercase and I get the same result. I already looked up the instructions and […]

## Congruence through Groups

I was reading proof and have gotten stuck in a place. I needed some help understanding a statement they have made: Let $G$ be a group of order $pqr$. Let $P,Q,R$ be Sylow subgroups of $G$ of order $p,q,r$ respectively. Let $\nu_p,\nu_q,\nu_r$ denote the number of Sylow subgroups of order $p,q,r$ respectively. Then, they have […]

Linear operators $P, Q, R$ on $\mathbb{R}^2$ have the following standard matrices: $$\frac{1}{5}\begin{bmatrix} 4 & 3 \\ -3 & 4 \end{bmatrix}, \quad \frac{1}{\sqrt{2}}\begin{bmatrix} -1 & 1 \\ 1 & 1 \end{bmatrix}, \quad \frac{1}{13}\begin{bmatrix} 9 & 6 \\ 6 & 4 \end{bmatrix}, $$ respectively. Explain the actions of these linear operators in geometric terms. Do we […]

I am having the same problem here while it is on the list actually. probably there is another mistake here is my code check it, please: base = [“a”,”b”,”c”,”d”,”e”,”f”,”g”,”h”,”i”,”j”,”k”,”l”,”m”,”n”,”o”,”p”,”q”,”r”,”s”,”t”,”u”,”v”,”w”,”x”,”y”,”z”] c= base.index(a) the a is input and I made sure it was “o”, “k” ValueError: [‘o’, ‘k’] is not in list Also, I can’t put the […]

## Path that meets every other path

In a directed graph $G$, what do we call a path, a sequence of edges $$(v_0,v_1),(v_1,v_2),\dots,(v_{n-1},v_n)$$ of length $n$, that intersects every other path of the same length $$(w_0,w_1),(w_1,w_2),\dots,(w_{n-1},w_n)$$ in the sense that for each such $w$ there is a $k$ with $v_k=w_k$? For instance, in a graph with two vertices $q$ and $r$ and […]