(use in a problem for junior) to practice. Can anyone share to me?
be an odd integer, 
.
integers 
such that for any 
,
and 
.
for which satisfy 
for some 
,
is greater than 
.
such that![\[f(x+yf(x))+f(xf(y)-y)=f(x)-f(y)+2xy\]](http://latex.artofproblemsolving.com/e/b/c/ebccae7e765d9fc3c8605e58a7399a70127b39b1.png)
, such that 
Prove that :
equality cases : ?
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Geoff Smith has asked to pass along some sad news to the Art of Problem Solving community -- Dan Schwarz (mavropnevma) has died.
As I'm sure we all know, Schwarz was a prolific poster on these forums. He was a huge contributor to the Romanian Masters in Mathematics and the European Girl's Math Olympiad, proposing many of the problems for both contests. Schwarz was also very involved with the math community in Romania as a whole, for example with the national olympiad and the Stars of Mathematics contest. His efforts and enthusiasm will be greatly missed by all.
Of course, to "thumbs-up" this post is to indicate respect for Schwarz.
As I'm sure we all know, Schwarz was a prolific poster on these forums. He was a huge contributor to the Romanian Masters in Mathematics and the European Girl's Math Olympiad, proposing many of the problems for both contests. Schwarz was also very involved with the math community in Romania as a whole, for example with the national olympiad and the Stars of Mathematics contest. His efforts and enthusiasm will be greatly missed by all.
Of course, to "thumbs-up" this post is to indicate respect for Schwarz.
This post has been edited 1 time. Last edited by v_Enhance, Jun 10, 2015, 12:46 AM
