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4h
reviewed Approve Decompose summation of signals
4h
answered Prove that: 1. $gcd(a,b)=lcm(a,b)$ iff $|a|=|b|$ 2. $k>0\implies lcm(ka,kb)=k lcm(a,bk)$ 3. $a\mid m, b\mid m$, then $lcm(a,b)\mid m$
4h
revised Prove that: 1. $gcd(a,b)=lcm(a,b)$ iff $|a|=|b|$ 2. $k>0\implies lcm(ka,kb)=k lcm(a,bk)$ 3. $a\mid m, b\mid m$, then $lcm(a,b)\mid m$
added 25 characters in body; edited title
14h
comment Show that $(1+\frac{1}{n})^n+\frac{1}{n}$ is eventually increasing
As usual, very nice!
1d
comment Missing values of the ratio $\frac{(x+y+z)^2}{x^2+y^2+z^2}$
Everything written above is correct. Then, we can start with a triple $(x,y,z)$ for which $\sum x^2 / \sum xy$ is an integer multiple of $3$ and $3\nmid xyz$..
1d
comment Missing values of the ratio $\frac{(x+y+z)^2}{x^2+y^2+z^2}$
Then you can set equivalently $a=b=j$ e $q=d=c=3n$. Does it really help?
1d
comment Missing values of the ratio $\frac{(x+y+z)^2}{x^2+y^2+z^2}$
Why do you think it is related to find the solutions of $ax^2+by^2=cz^2$?
1d
answered For what values of $n$ , does $7 \mid 5^n+1$
1d
asked Missing values of the ratio $\frac{(x+y+z)^2}{x^2+y^2+z^2}$
2d
comment Each number in $S\subseteq \{1,\ldots,2n\}$ does not divide another one, with $|S|= n$. In how many ways?
Again, very clear and simple! Thank you Robert
2d
accepted Each number in $S\subseteq \{1,\ldots,2n\}$ does not divide another one, with $|S|= n$. In how many ways?
Aug
26
revised Each number in $S\subseteq \{1,\ldots,2n\}$ does not divide another one, with $|S|= n$. In how many ways?
added 131 characters in body
Aug
25
revised Each number in $S\subseteq \{1,\ldots,2n\}$ does not divide another one, with $|S|= n$. In how many ways?
added 182 characters in body
Aug
25
comment Product property of Big O
Well, big-O usually is defined in terms of absolute value; apart of this fact, your proof is basically correct.
Aug
25
revised Each number in $S\subseteq \{1,\ldots,2n\}$ does not divide another one, with $|S|= n$. In how many ways?
added 95 characters in body
Aug
25
asked Each number in $S\subseteq \{1,\ldots,2n\}$ does not divide another one, with $|S|= n$. In how many ways?
Aug
25
comment For all $n$ there exists $x$ such that $\varphi(x)<\varphi(x+1)<\ldots<\varphi(x+n)$
I agree this would solve the question, but how do you prove it?
Aug
25
accepted Each number in a subset $S\subseteq \{1,\ldots,2n\}$ does not divide another one. Then $\max |S|$?
Aug
25
comment Each number in a subset $S\subseteq \{1,\ldots,2n\}$ does not divide another one. Then $\max |S|$?
I lost the trivial solution $\{n+1,\ldots,2n\}$, indeed :(
Aug
25
comment Each number in a subset $S\subseteq \{1,\ldots,2n\}$ does not divide another one. Then $\max |S|$?
@AndréNicolas 100 or 1000 does not make so much difference; do you have the link of thread you are talking?