[/quote]
,
such that 
and 
are both perfect squares.
be reals such that 
and 
Prove that
Where 
with 
,
integers obtained by arranging four digits 
in some order, are all not divisible by 
.
grid, and in each cell, there is a coin with one side white, and other side black. We start by all coin facing white. Alice and Bob executes the following operation:
pairwise distinct cells, and turn over all of the coins in those cells. Next, Bob chooses one row or column, and turn over all of the coins in that row, or column.
with the following property:
turns.
be a triangle with integer side lengths. Let 
be points on segment 
such that 
are in this order, 
,
.
and 
,
.
.
points of 
is good in the figure.
of tiles with side length 
,
,
Each vertex of the tiles are on good points, and
tiles, such that it forms a equilateral triangle of side length 
such that ![\[
l^2+mn=m^2+ln,\quad n^2+lm=2020,\quad l\le m\le n.
\]](http://latex.artofproblemsolving.com/9/1/1/911d942d5f8afc7a230b7e3ab7082f9975a72b32.png)
unitsquare, using L and X.
created by removing the unitcube at the cornor of the cube with side length 
.
created with four unitcube, and infinitely many unitcubes.
Y by
I found some questions hard to solve by myself, so I went on AoPS
I know that ZetaX said that do not repost questions(https://artofproblemsolving.com/community/c6h135914_zero_tolerance), so I searched on the "Advanced Search". I didn't found it, so I posted it.
However, somebody always founded that I reposted, so I am very...well, upset?
Can anyone tell me how to search problems better on AoPS?
I know that ZetaX said that do not repost questions(https://artofproblemsolving.com/community/c6h135914_zero_tolerance), so I searched on the "Advanced Search". I didn't found it, so I posted it.
However, somebody always founded that I reposted, so I am very...well, upset?
Can anyone tell me how to search problems better on AoPS?
