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be the set of real numbers. Determine all functions 
such that ![\[ f(x^2 - y^2) = x f(x) - y f(y) \]](http://latex.artofproblemsolving.com/6/8/f/68f78e0df627f6ac04052433c01627bf16f0af8e.png)
for all pairs of real numbers 
and 
.
into 
or 
can sometimes be quite complex. That's why I’ve written a program to assist with this process.
be real numbers such that 
Prove that 
Where 
and 
be points on a plane such that 
, where 
is a positive integer. Let 
be the set of all points 
such that 
, where 
is a real number. The path that traces is continuous, and the value of is minimized. Prove that is rational for all positive integers 
be reals such that 
. Prove that
Let be reals such that 
. Prove that
be non-negative real numbers such that 
. Find the maximum and minimum values of the expression![\[
P = \frac{a}{a^2 + 2} + \frac{b}{b^2 + 2} + \frac{c}{c^2 + 2}.
\]](http://latex.artofproblemsolving.com/d/b/e/dbea7db769c4996fc081ee75837e177b298cffcb.png)
. Find the minimum and maximum values of 
+ 
+ 
Find the maximum positive integer 
such that for every subset 
with n elements, there always exist two elements a, b in T such that:
where 
and 
are polynomials with integer coefficients. Then 
for 
. If the polynomials 
and hence 
would be of degree 
, then 
is identically 
, since it has n roots. Hence, we would have 
. This is a contradiction since the coeff. of 
on the left is 
, on the right 
.
Find 
are distinct integers, cannot be written as the product of two non-constant polynomials with integer coefficients, i.e, it is irreducible.
