Try this beautiful problem from the PRMO, 2017 based on GCD and Primes.
For each positive integer n, consider the highest common factor \(h_n\) of the two numbers n!+1 and (n+1)! for n<100, find the largest value of \(h_n\).
GCD
Primes
Inequalities
Answer: is 97.
PRMO, 2017, Question 29
Elementary Number Theory by David Burton
n! +1 is not divisible by 1,2,.....,n (n+1)! divisible by 1,2,....,n then \(hcf \geq (n+1)\) and (n+1)! not divisible by n+2, n+3,...... then hcf= (n+1)
let n=99, 99! +1 and (100)! hcf=100 not possible as 100 |99! and 100 is non prime
let n=97 96! + 1 and 97! both divisible by 97 then hcf=97.
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 […]
In 2025, 8 students from Cheenta Academy cracked the prestigious Regional Math Olympiad. In this post, we will share some of their success stories and learning strategies. The Regional Mathematics Olympiad (RMO) and the Indian National Mathematics Olympiad (INMO) are two most important mathematics contests in India.These two contests are for the students who are […]
Cheenta Academy proudly celebrates the success of 27 current and former students who qualified for the Indian Olympiad Qualifier in Mathematics (IOQM) 2025, advancing to the next stage — RMO. This accomplishment highlights their perseverance and Cheenta’s ongoing mission to nurture mathematical excellence and research-oriented learning.