# Tagged Questions

1answer
26 views

### Generalized Pythagorean triples construction.

All primitive Pythagorean triples $(a, b, c) : \{ a^2 + b^2 = c^2 \} \wedge \{ a \equiv 0 \pmod{2} \}$ can be expressed in the form:$$\{ a = 2pq, b = p^2 - q^2, c = p^2 + q^2 \}$$ for positive ...
0answers
56 views

### A starting point for the Erdos-Straus Conjecture [closed]

According to the Erdos-Straus conjecture, could we consider the following as a new approach? $$\frac{4}{n}=\frac{1}{n^2}+\frac{1}{n^2}+\frac{1}{n^2}+\frac{\lambda}{n^2},$$ where $\lambda=n+3(n-1).$ ...
2answers
34 views

### Proof for: GCD and divisibility

I need some hints how to proof something like the following: Let $a,b \in \mathbb{Z}$ with $a,b \not= 0$ and let $\gcd(a,b)=d$. (1) For any $m,n\in \mathbb{Z}$ we have $d \mid ma+nb$. (2) There ...
0answers
37 views

### Proof of two properties of a simple math function

I would like to define a function to evaluate the value for some entities which receive a number of "up"s ($\mathcal{u}$) and "down"s ($\mathcal{d}$). I devised the following function: ...
1answer
35 views

### The set of all real numbers $\epsilon$ with $0 < \epsilon < 1$ is equinumerous with the set of all sets of positive integers

How is a proof like this normally conducted? I know that Cantor's theorem may prove useful here, but I'm having trouble extending the definition to problems that are (seemingly) unrelated.
1answer
28 views

### Show that the set of all subsets of an infinite enumerable set is not enumerable

I know this problem involves using Cantor's theorem, but I'm not sure how to show that there are more subsets of an infinite enumerable set than there are positive integers. It seems like a lot of ...
2answers
72 views

### Tough Turing machine multiple choice questions

I'm having a tough time deciding whether my answers for these questions are correct. Can anyone help me agree on something? They seem pretty easy, but I've found that they're actually difficult. ...
1answer
54 views

### Show that $gcd(x,y)$ and $z = lcm(x,y)$ is primitive recursive

For the $gcd(x,y)$ we note: $gcd(x,0) = x$ $gcd(x,succ(y)) = gcd(succ(y),mod(x,succ(y)))$ $succ(x)$ and $mod(x,y)$ are both primitive recursive, so $gcd(x,y)$ must be as well. $z = lcm(x,y)$ if ...
2answers
72 views

### Show that, given regular expression $R$, we can decide whether $L(R)$ is prefix-free

Suppose language $L$ is called prefix-free if no member is a proper prefix of another. For instance, cat is a proper prefix of category and so $L = \{cat,category,ego,go,rye\}$ is not prefix free. ...
1answer
177 views

2answers
324 views

### Resource for Vieta root jumping

I can't seem to find a good resource on Vieta's root jumping, which would explain various scenarios that suggest using the technique. Does anyone have a suggestion for a reference?