## 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: 5210

### 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: 5020

### 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: 5020

### 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: 5210

### 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: 7066

### 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: 7066

### 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: 7066

### 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: 3887

### Integer

Find all natural numbers $(a,b)$ such that
$\frac{b^2+a}{ab-1}$ in an integer.
Wed Dec 27, 2017 4:16 am
Forum: Number Theory
Topic: Integer
Replies: 1
Views: 3781

### Integer

Find all natural numbers $(a,b)$ such that
$\frac{b^2+a}{ab-1}$ in an integer.
Wed Dec 27, 2017 4:11 am
Forum: Site Support
Topic: Help me please
Replies: 1
Views: 7344

### 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? 