[/quote]
,
and 
are situated 
units apart on a level surface. Find the set of all points on the surface which are so situated that the angles of elevation of the tops of the poles are equal.
with 
odd, which satisfy the equation:
denote the set of all real numbers. Find all functions 
such that ![\[ f\left( x^{2}+f(y)\right) =y+\left( f(x)\right) ^{2}\hspace{0.2in}\text{for all}\,x,y\in \mathbb{R}. \]](http://latex.artofproblemsolving.com/8/5/c/85c37ee472f918eace12c8cd7bef6766e617d2aa.png)
(where 
are the digits and 
)
For example the permutation sum of 20253 is 
Let 
and 
be two fivedigit integers with the same permutation sum.
.
pairwise distinct positive integer numbers 
,![\[
\frac{a_i^2 + a_j^2}{a_i + a_j}
\]](http://latex.artofproblemsolving.com/3/5/3/3537ddec6d793d3831ba82a1e13b98d43b1c29bc.png)
that satisfy![\[
f(x^2-y)+2yf(x)=f(f(x))+f(y)
\]](http://latex.artofproblemsolving.com/f/b/b/fbb693770cd90d8a144026608074122e54da5802.png)
for all 
.
be the incircle of triangle 
.
is parallel to side 
and tangent to 
is parallel to side 
and tangent to 
,
satisfy all conditions below:
for all 
for all 
for all 
that are solutions of the equation 
.
Y by
Hello everyone, these days I have a burning urge to pick up new math concepts because I think they are important/interesting. But I also feel a constant burnout where I get really tired when I try to solve math problems of these new concepts. I can't and then it gets very demotivating. I don't want to take a break from math because solving problems have become such a natural part of me and also I really want to qualify for usamo next year (my last year I can since it's senior yr). Any suggestions?
