jordan
Reputation
1,335
Next privilege 2,000 Rep.
 Jun7 comment How to generate a random number between 1 and 10 with a six-sided die? .....Jack show! Jun6 comment How many integers $\{xy \colon 1\le x\le y\le 2x\}$? The distribution of integers with a divisor in a given interval , Annals of Math. (2) 168 (2008), 367-433, Kevinf Ford [Corollary 3]: it is an atomic bomb, but yes it works, very thanks! Jun6 revised How many integers $\{xy \colon 1\le x\le y\le 2x\}$? edited title Jun5 accepted Splitting the asymptotic upper density Jun5 asked Splitting the asymptotic upper density Jun4 accepted How many integers $\{xy \colon 1\le x\le y\le 2x\}$? May29 answered Find the sequence of partial sums for the series $a_n = (-1)^n$ Does this series converge? May19 comment Approximating $e^{x}/(e^{x} - 1)$ It depends where you'd like to approximate it ;) May18 asked How many integers $\{xy \colon 1\le x\le y\le 2x\}$? May6 revised Filtering a sum of reciprocal of integers added 110 characters in body May6 accepted Only finitely many $a, b$ such that $2+3^n+5^{n^2}=2^a7^b$ for some $n$? May6 revised Filtering a sum of reciprocal of integers added 14 characters in body; edited title May6 asked Filtering a sum of reciprocal of integers May2 comment Only finitely many $a, b$ such that $2+3^n+5^{n^2}=2^a7^b$ for some $n$? If it is a solution for a fixed $n$, then it is exactly one: it is asked to prove that there exist only finitely many $n$ such that the dophantine equation has (a) solution.. May2 answered Check the convergence of $a_{n+1}=\sqrt{a_n+\frac{4}{a_n}}$ where $a_1=4$ May2 asked Only finitely many $a, b$ such that $2+3^n+5^{n^2}=2^a7^b$ for some $n$? May2 answered If $m, n$ be positive integers, prove that $\phi(mn)=\phi((m,n))\phi([m,n])$, where $(m,n)=$ gcd of $m, n$ and $[m, n]=$ lcm of $m, n$. May2 comment If $m, n$ be positive integers, prove that $\phi(mn)=\phi((m,n))\phi([m,n])$, where $(m,n)=$ gcd of $m, n$ and $[m, n]=$ lcm of $m, n$. Oh I see now that (6,9) is not a counterexample for the new problem. Wait, I put it in a new answer May1 comment If $m, n$ be positive integers, prove that $\phi(mn)=\phi((m,n))\phi([m,n])$, where $(m,n)=$ gcd of $m, n$ and $[m, n]=$ lcm of $m, n$. Indeed, he asks for $\varphi(m)\varphi(n)$, not $\varphi(mn)$ [recall that they are equal if and only if m and n are coprime, as expected..] Apr30 comment If $m, n$ be positive integers, prove that $\phi(mn)=\phi((m,n))\phi([m,n])$, where $(m,n)=$ gcd of $m, n$ and $[m, n]=$ lcm of $m, n$. I have the fifth edition.. Can you check where is it exactly?