Try this beautiful problem from the American Invitational Mathematics Examination I, AIME I, 1992 based on Rational Numbers.
Find the sum of all positive rational numbers that are less than 10 and that have denominator 30 when written in lowest terms.
Integers
Rational Numbers
Euler's Totient Function
Answer: is 400.
AIME I, 1992, Question 1
Elementary Number Theory by David Burton
For Euler's Totient function, there exists 8 numbers that are relatively prime to 30, less than 30.
Here they are in (m,30-m) which in the form of sums of 1
\(\Rightarrow\) sum of smallest eight rational numbers=4
there are eight terms between 0 and 1 and there are eight terms between 1 and 2 where these we get as adding 1 to each of first eight terms
\(\Rightarrow\) 4(10)+8(1+2+3+...+9)=400.
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad
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 […]