2002 Indonesia MO Problems
Show that is divisible by for any integers .
Five regular dices are thrown, one at each time, then the product of the numbers shown are calculated. Which probability is bigger; the product is or the product is ?
Find all real solutions from the following system of equations:
Given a triangle with . On the circumcircle of triangle there exists point , which is the midpoint of arc that contains . Let be a point on such that is perpendicular to . Prove that .
Nine of the following ten numbers: are going to be filled into empty spaces in the table shown below. After all spaces are filled, the sum of the numbers on each row will be the same. And so with the sum of the numbers on each column, will also be the same. Determine all possible fillings.
Find all prime number such that and are also prime.
Let be a rhombus with , and is the intersection of diagonals and . Let , , and are three points on the rhombus' perimeter. If is also a rhombus, show that exactly one of , , and is located on the vertices of rhombus .
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