Random Problems
108
Find all integer solutions to .
191
Two given circles intersect in two points and
. Show how to construct a segment
passing through
and terminating on the two circles such that
is a maximum.
70
Let be a prime number. Prove that there exists an integer
such that
if and only if there exists an integer
such that
.
167
Prove that the right circular cylinder of volume which has the least surface area is the one whose diameter is equal to its altitude.
186
What is the greatest possible area of an octagon with all sides equal to 12?