Try this beautiful interesting problem based on Number Theory from PRMO 2016 Problem 2.
The five digit number $2 a 9 b 1$ is a perfect square. Find the value of $a^{b-1}+b^{a-1}$.
Properties of Perfect Squares
Divisibility Rules of different numbers
Finding the square root of a number
Challenge and Thrill of Pre College Mathematics
PRMO 2016
50
An odd perfect square is of the form $8k+1$
Hence $8| 2a9b0$
Hence $8 | 2a000 + 9b0 $
$8 | 900 +b0 $
$ 8 | b4$
Therefore the possible values of b are $6,2$
So possible numbers are $2a921,2a961$
Now check for the possible values of $a$ and calculate the square root to check if it is a perfect square
The only valid solution is $a=5$
Hence calculate the required expression.
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 […]