Ημέρα 1η
, there exist three that are the side lengths of an acute triangle.
2. A circle is divided into 
congruent arcs by points. The points are colored in four colors such that some 
points are colored Red, some points are colored Green, some points are colored Blue, and the remaining points are colored Yellow. Prove that one can choose three points of each color in such a way that the four triangles formed by the chosen points of the same color are congruent.
congruent arcs by points. The points are colored in four colors such that some points are colored Red, some points are colored Green, some points are colored Blue, and the remaining points are colored Yellow. Prove that one can choose three points of each color in such a way that the four triangles formed by the chosen points of the same color are congruent. 3. Determine which integers 
have the property that there exists an infinite sequence 
of nonzero integers such that the equality 
holds for every positive integer 
.
have the property that there exists an infinite sequence of nonzero integers such that the equality holds for every positive integer .Ημέρα 2η
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