Το 10ο Πρόβλημα του Hilbert, το δέκατο στη σειρά από τα 23 προβλήματα που έθεσε ο David Hilbert το 1900 ως οδηγό για τους μαθηματικούς του 20ού αιώνα ζητούσε:
for which is divisible by all positive integers whose cube is not greater than 
We want to partition 
into two disjoint sets such that both sets do not contain two different numbers whose sum is a power of 
Find the number of such partitions. 
be a chord of the circle 
not passing through its center and let 
be the midpoint of 
Let 
be a variable point on different from 
and 
and 
be the point of intersection of the tangent lines at of circumcircle of 
and at of circumcircle of 
Show that all 
lines pass through a fixed point. for which 
satisfying 
} . Find the number of numbers of 6 digits which cantain 
or 's digit and they is permulated (For example 137456 and 314756 is one numbers). 
is not isosceles triangle. 
and 
its incenter and circumcenter. The incircle tangents to 
at a point 
. The circumcircle of 
intersects 
at 
. Prove that 
, where 
is radius of incircle of . 
and lie a circle. 
. 
and 
incenters of 
. 
midpoints of arcs 
. Then prove that 
are concurrent.
