Sum of digits | PRMO 2019 | Question 20
Try this beautiful problem from the Pre-RMO, 2019 based on Sum of digits.
Sum of digits - PRMO 2019
Consider the set E of all natural numbers n such that when divided by 11,12,13 respectively, the remainders, in that order, are distinct prime numbers in an arithmetic progression. If N is the largest number in E, find the sum of digits of N.
- is 107
- is No largest value
- is 840
- cannot be determined from the given information
Key Concepts
Largest Number
Divisibility
Integer
Check the Answer
Answer: is No largest value.
PRMO, 2019, Question 20
Elementary Number Theory by David Burton
Try with Hints
here N can be of the form (13)(12)(11)(k)+29
where k belongs to an integer
then no largest value.
Other useful links
- https://cheenta.com/rational-number-and-integer-prmo-2019-question-9/
- https://www.youtube.com/watch?v=lBPFR9xequA