| 1 | Let  be two positive sequences defined by  and for all  .Prove that they are converges and find their limits. | |
| 2 | Given the polynomial  where  is a positive integer. Prove that  can't be written as a product of  non-constant polynomials with integer coefficients. | |
| 3 | Given a regular 103-sided polygon. 79 vertices are colored red and the remaining vertices are colored blue. Let  be the number of pairs of adjacent red vertices and  be the number of pairs of adjacent blue vertices.a) Find all possible values of pair  b) Determine the number of pairwise non-similar colorings of the polygon satisfying  2 colorings are called similar if they can be obtained from each other by rotating the circumcircle of the polygon. | |
| 4 | Let  be an acute triangle,  be the circumcircle, and  Let  be the midpoint of arc  (not containing ).  lies on   such that   intersects at the second point   and intersects  at   intersects  at  a) Prove that  b)  lies on such that  is parallel to   intersects at  The circumcircle of triangle  intersects at the second point  Prove that  passes through the midpoint of segment | |
| 1 | Given a circle and two fixed points  on  and an arbitrary point on such that the triangle is acute. lies on ray   lies on ray such that  and  Let  be the intersection of  and    intersects at  a) Prove that  are collinear.b)  is the midpoint of  Let be the intersection of  and    is the line passing through and perpendicular to   is the intersection of and  intersects at   Prove that  passes through a fixed point. | |
| 2 | Find the maximum of where  are positive real numbers. | |
| 3 | Find all sets of not necessary distinct 2014 rationals such that:if we remove an arbitrary number in the set, we can divide remaining 2013 numbers into three sets such that each set has exactly 671 elements and the product of all elements in each set are the same. | |
Publishing original scientific research in a peer-reviewed journal is an achievement many scholars work toward for years. Achieving this feat early in one's academic journey requires exceptional intellectual rigor, creativity, and persistence. Aaditya Punatar and Muskan Sadana have reached this remarkable milestone, successfully publishing their collaborative research paper in the prestigious Journal of Emerging Investigators […]
Her project on quantum-accelerated Steiner trees for 15-minute cities earned a place among the finalists at the world's largest pre-college STEM competition. Prishaa Shrimali of Marymount School of New York, was selected as a Grand Finalist at the 2026 Regeneron International Science and Engineering Fair (ISEF) in Phoenix, Arizona. Her project was Optimizing Urban Accessibility: […]
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's M.Stat Entrance. They ranked within the first 50 in the entire country in these entrances. I.S.I. M.Stat Entrance
In 2026, the following Cheenta students have been successful for Indian Statistical Institute's B.Stat Entrance and Chennai Mathematical Institute's B.Sc. Math Entrance. They ranked within the first 200 in the entire country in these entrances. Most of these students attended the problem solving workshops regularly, which happen 5 days every week. CMI B.Sc. Math Entrance […]
