[/quote]
,
be the set of black cells at the end of the game. Ali and Shayan respectively aim to minimize and maximise the perimeter of the shape 
called ‘nice’ if and only if 
and 
are both perfect squares. How many positive integers 
such that 
are composites for all nice numbers 
?
decide whether there exist pairwise distinct positive integers 
such that for every 
,
divides 
.
of positive integers with the following property: all of the terms of the sequence 
have a greatest common divisor 
be real numbers such that 
find the largest value of 
such that 
and 
are all perfect square.
be pairwise coprime positive integers with 
being prime and 
.![$I = [0, a_1 a_2 \cdots a_n ]$](http://latex.artofproblemsolving.com/a/2/b/a2bce96b048c9b8fc94926db80aba37fd5037b4a.png)
of the real line, mark all integers that are divisible by at least one of the numbers 
. These points split 
into a number of smaller segments. Prove that the sum of the squares of the lengths of these segments is divisible by 
such that ![\[f(xy-1)+f(x)f(y)=2xy-1,\]](http://latex.artofproblemsolving.com/8/8/8/888ca39f2b7f8cec6d6426bee28d40eade40a66e.png)
for any real numbers 
and 
be a regular polygon, and let 
be its set of vertices. Each point in 
Y by PikaPika999
Hello.
i finished intro to geo textbook and class a few months ago, I was wondering what geo to do next. I took a quick look at egmo, and i figured i should probably do more before starting it. Does anyone have any resources they have that could help with int geo?
Thanks!
i finished intro to geo textbook and class a few months ago, I was wondering what geo to do next. I took a quick look at egmo, and i figured i should probably do more before starting it. Does anyone have any resources they have that could help with int geo?
Thanks!
i can understand.
