Find all prime numbers of the form
, where n is a natural number.Problème2:
Let the quadruangle
be inscribed in a circle of radius 1.
Prove that the difference between its perimeter and the sum of the lengths of its diagonals is positive and less than 4.Problème3:
Let a, b and c be positive real numbers for which the equality
Prove that the inequality
When dos equality holds?Problème4:
Find all prime numbers p and q which satisfy the equation
points in the plane are given such that every three of them are nor colinear. Prove that there exists a triangle such that all the points are in its interior, and on each of its sides lies exactly one point of the given points.Bonne chance.