3k views

### Is a number meeting these conditions divisible by forty-nine?

I am not a mathematician, I'm a linguistics PhD student. As part of my research I need to put various convoluted sentences through various syntactic transformations and see then check whether people ...
1k views

### Looking to Acquire Intution Regarding the Fundamental Theorem of Arithmetic

I'm sorry ahead if time if this is overly trivial for this site. Currently in school, much of what I enjoy is number theory - based. Currently, I lean pretty heavily on the FTA for a good deal of my ...
34k views

### If $\gcd(a,b)=1$ and $a$ and $b$ divide $c$, then so does $ab$

Using divisibility theorems, prove that if $\gcd(a,b)=1$ and $a|c$ and $b|c$, then $ab|c$. This is pretty clear by UPF, but I'm having some trouble proving it using divisibility theorems. I was ...
344 views

### Are there any integer solutions to $a^3=b^2$?

I was wondering if there were any two integers $a$ and $b$ where $a^3=b^2$.
2k views

### If $\gcd(a,b)=d$, then $\gcd(ac,bc)=cd$?

$A$ an integral domain, $a,b,c\in A$. If $d$ is a greatest common divisor of $a$ and $b$, is it true that $cd$ is a greatest common divisor of $ca$ and $cb$? I know it is true if $A$ is a UFD, but can'...
324 views

### Is my proof that the square root of all imperfect squares are irrational correct?

I was answering a Quora question about whether $\sqrt{13}$ is irrational or not (link if needed), and I tried to prove that, in fact, the square root of all imperfect squares are irrational. This is ...
229 views

### Rings where divisors of $mn$ are product of divisors of $m$ and $n$; relation to UFDs

Using the fundamental theorem of arithmetic, it's easy to prove this proposition: Proposition. Every divisor of $mn$ can be written as the product of a divisor of $m$ to a divisor of $n$. My ...