AoPS Academy
[/quote]
, do not answer with "
is a solution" only. Either you post any kind of proof or at least something unexpected (like "
is the smallest solution). Someone that does not see that is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
decide whether there exist pairwise distinct positive integers 
such that for every 
, 
divides 
.
of four distinct positive integers, we denote the sum 
by 
. Let 
denote the number of pairs 
with 
for which 
divides . Find all sets 
of four distinct positive integers which achieve the largest possible value of .
is the center of the circle. If three angles 
and 
be equal, find 
square is filled with numbers 
.The numbers inside four 
squares is summed,and arranged in an increasing order. Is it possible to obtain the following sequences as a result of this operation?
consecutive even numbers, such that the square of their product is divisible by the sum of their squares.
points on the plane. No three of them lie on the same straight line and no four lie on the same circle. Prove that it is possible to split these points into 
pairs and cover each pair of points with a circle containing no other points.
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