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 
Y by Adventure10
Prove that for every point 
on the surface of a regular tetrahedron there exists a point 
such that there are at least three different curves on the surface joining to with the smallest possible length among all curves on the surface joining to .
on the surface of a regular tetrahedron there exists a point 
such that there are at least three different curves on the surface joining to with the smallest possible length among all curves on the surface joining to .
