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# Category Archives: Kazakhstan

## [Soln] 2015 Kazakhstan NMO Problem 5

2015 Kazakh NMO 5. Find all possible permutations of so that when then we have and when then we have . Here .

## 2015 Kazakhstan NMO Problem 5

## [Soln] 2015 Kazakhstan NMO Problem 4

2015 Kazakh NMO 4. is the product of all positive divisors of that are divisible by (the empty product is equal to 1). Show that is a perfect square, for any positive integer .

## 2015 Kazakhstan NMO Problem 4

## [Soln] 2015 Kazakhstan NMO Problem 3

2015 Kazakh NMO 3. A rectangle is said to be inscribed in a triangle if all its vertices lie on the sides of the triangle. Prove that the locus of the centers (the meeting points of the diagonals) of all rectangles which … Continue reading