[/quote]
,
.
and 
of 
are said to be friends if the following conditions are true:
elements.[/quote]
be positive real numbers. Prove that ![\[108\cdot(ab+bc+ca)\leqslant(\sqrt{a+b}+\sqrt{b+c}+\sqrt{c+a})^4.\]](http://latex.artofproblemsolving.com/0/2/7/027279b75a2b5b2bb71200d315ff4a77b7701aa3.png)
be reals such that 
Show that
Let 
and 
Show that
Let 
and 
.
satisfy that: 
.
and 
Find the value range of 
distinct divisors of a positive integer number 
form an arithmetic progression. Prove that the number 
divisors.
be distinct real numbers such that 
Find the value of 
Find the value of 
Find the value of 
Y by
For a 
chessboard, Use L tetrominos to tile it. you can spin it, but not flip it, and no two tetrominos must overlap. For how many blocks on the board, we can eradicate it so that the rest of the chessboard can be fully covered? I mean to say that for which squares can be left out for any n. For example, when 
, the four squares at the corners can be cut off so the rest can be covered, or the one in the middle, but no other square.
chessboard, Use L tetrominos to tile it. you can spin it, but not flip it, and no two tetrominos must overlap. For how many blocks on the board, we can eradicate it so that the rest of the chessboard can be fully covered? I mean to say that for which squares can be left out for any n. For example, when 
, the four squares at the corners can be cut off so the rest can be covered, or the one in the middle, but no other square.
squares need to be removed. We show a construction for 
which can be extended repeatedly to get the desired result.
