TIFR 2014 Problem 30 Solution is a part of TIFR entrance preparation series. The Tata Institute of Fundamental Research is India's premier institution for advanced research in Mathematics. The Institute runs a graduate programme leading to the award of Ph.D., Integrated M.Sc.-Ph.D. as well as M.Sc. degree in certain subjects.
The image is a front cover of a book named Topics in Algebra by I.N.Herstein. This book is very useful for the preparation of TIFR Entrance.
Also Visit: College Mathematics Program
How many maps $\phi: \mathbb{N} \cup {0} \to \mathbb{N} \cup {0}$ are there satisfying $\phi(ab)=\phi(a)+\phi(b)$ , for all $a,b\in \mathbb{N} \cup {0}$ ?
Take $n\in \mathbb{N} \cup {0}$.
By the given equation $\phi(n\times 0)=\phi(n)+\phi(0)$.
This means $\phi(0)=\phi(n)+\phi(0)$.
Oh! This means $\phi(n)=0$. $n\in \mathbb{N} \cup {0}$ was taken arbitrarily. So...
$\phi(n)=0$ for all $n\in \mathbb{N} \cup {0}$.
There is only one such map.
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 […]
