Tag Archives: Kazakh NMO

[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 .

Posted in Grade 12, Kazakhstan | Tagged , , | Leave a comment

[Hints] 2015 Kazakhstan NMO Problem 5

Posted in Grade 12, Kazakhstan | Tagged , , | Leave a comment

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 .

Posted in Grade 12, Kazakhstan | Tagged , , | Leave a comment

[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 .

Posted in Grade 12, Kazakhstan | Tagged , , | Leave a comment

[Hints] 2015 Kazakhstan NMO Problem 4

Posted in Grade 12, Kazakhstan | Tagged , , | Leave a comment

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 .

Posted in Grade 12, Kazakhstan | Tagged , , | Leave a comment

[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

Posted in Grade 12, Kazakhstan | Tagged , , | Leave a comment