1 Let 
be 
pairwise distinct prime numbers. Show that the sum
is not a unit fraction 
of some integer square number.
2 Determine all triples
of real numbers such that the following system of equations holds true:
3 Let 
be a circle centered at 
and let 
be a tangentline to through some point 
. Let 
be a point on and let 
be a line through intersecting at 
and 
. Let 
be the point on bisecting the arc 
not containing 
and let 
be the the image of under a reflection over 
.
Prove that, , and are vertices of a trapezoid.
4 Define the sequence
of positive integers by 
and the condition that 
is the least integer such that
Determine the set of elements of 
.
be pairwise distinct prime numbers. Show that the sumis not a unit fraction of some integer square number. 2 Determine all triples
of real numbers such that the following system of equations holds true: be a circle centered at and let be a tangentline to through some point . Let be a point on and let be a line through intersecting at and . Let be the point on bisecting the arc not containing and let be the the image of under a reflection over .Prove that
, , and are vertices of a trapezoid. 4 Define the sequence
of positive integers by and the condition that is the least integer such that Determine the set of elements of . 
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