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



Check the Answer

But try the problem first…

Answer: is No largest value.

Suggested Reading

PRMO, 2019, Question 20

Elementary Number Theory by David Burton

Try with Hints

First hint

here N can be of the form (13)(12)(11)(k)+29

Second Hint

where k belongs to an integer

Final Step

then no largest value.

Subscribe to Cheenta at Youtube