## Search found 47 matches

- Thu Nov 22, 2018 9:34 pm
- Forum: Algebra
- Topic: a+b+c>=1/a+1/b+1/c
- Replies:
**3** - Views:
**1361**

### Re: a+b+c>=1/a+1/b+1/c

Please someone...

- Tue Apr 24, 2018 12:11 am
- Forum: Algebra
- Topic: FE from USAMO 2002
- Replies:
**4** - Views:
**939**

### Re: FE from USAMO 2002

Ahh, I'm not sure. But I try: You show that $f(-x^2)=-xf(x)$ but we know also that $f(x^2)=xf(x)$ so $-f(-x^2)=f(x^2)$ and so $f(-x^2)=-f(x^2)$ and if we put $x^2=a$ we obtein $f(-a)=-f(a)$ but we know that $f(x^2-y^2)=xf(x)-yf(y)$ for positive real numbers; so using the fact that $f(-x^2)=-xf(x)$ t...

- Mon Apr 23, 2018 11:31 am
- Forum: Algebra
- Topic: FE from USAMO 2002
- Replies:
**4** - Views:
**939**

### Re: FE from USAMO 2002

The fact that $f(x^2)=xf(x)$ implies that $f(x^2-y^2)=f(x^2)-f(y^2)$ so it implies that $f(a-b)=f(a)-f(b)$ for $a$ and $b$ positive perfect square; why do you say that this expression is true also for $a$ and $b$ positive numbers (and so no necessary positive perfect squares...)? And why after do yo...

- Sat Apr 21, 2018 10:55 pm
- Forum: Algebra
- Topic: a+b+c>=1/a+1/b+1/c
- Replies:
**3** - Views:
**1361**

### Re: a+b+c>=1/a+1/b+1/c

Someone? Pleasee

- Sat Apr 21, 2018 10:53 pm
- Forum: Algebra
- Topic: Inequality with a,b,c sides of a triangle
- Replies:
**7** - Views:
**1743**

### Re: Inequality with a,b,c sides of a triangle

Yes, now understand. Very gentle Atonu!

- Sat Apr 21, 2018 10:26 pm
- Forum: Algebra
- Topic: Inequality with a,b,c sides of a triangle
- Replies:
**7** - Views:
**1743**

### Re: Inequality with a,b,c sides of a triangle

Thanks Atonu, now is clear! :) Only a doubt, can you put a link where is wrote the property that you say? Because I found that the exponent ($n$) must be positive, yes in your cases the numbers are positive but where is wrote? I saw here but I didn't find the property that you say... :( https://en.m...

- Fri Apr 20, 2018 10:24 pm
- Forum: Algebra
- Topic: Inequality with a,b,c sides of a triangle
- Replies:
**7** - Views:
**1743**

### Re: Inequality with a,b,c sides of a triangle

Sorry Atonu, but I don't understand some passages... :( Why exactly $$\sum_{cyc} \frac{\sqrt{b+c-a}}{\sqrt{b}+\sqrt{c}-\sqrt{a}}= \sum_{cyc} \sqrt{1- \frac{(x-y)(x-z)}{2x^2}} \le \sum_{cyc} 1-\frac{(x-y)(x-z)}{4x^2} = 3 - \frac{1}{4} \sum_{cyc} x^{-2}(x-y)(x-z) $$ ? And how do you use exactly Shur's...

- Wed Dec 27, 2017 4:17 am
- Forum: Number Theory
- Topic: Integer
- Replies:
**1** - Views:
**682**

### Integer

Find all natural numbers $(a,b)$ such that

$\frac{b^2+a}{ab-1}$ in an integer.

$\frac{b^2+a}{ab-1}$ in an integer.

- Wed Dec 27, 2017 4:16 am
- Forum: Number Theory
- Topic: Integer
- Replies:
**1** - Views:
**594**

### Integer

Find all natural numbers $(a,b)$ such that

$\frac{b^2+a}{ab-1}$ in an integer.

$\frac{b^2+a}{ab-1}$ in an integer.

- Wed Dec 27, 2017 4:11 am
- Forum: Site Support
- Topic: Help me please
- Replies:
**1** - Views:
**657**

### Help me please

Since some days in this forum I see the post not clear, It means that I see only "$"

someone can resolve this problem? Another people have the same problem?

someone can resolve this problem? Another people have the same problem?